@ARTICLE{drake-original,
AUTHOR = {F.R. Drake},
TITLE = {How Recent Work in Mathematical Logic Relates to the Foundations of Mathematics},
JOURNAL = {The Mathematical Intelligencer},
YEAR = {1985}
}
@INPROCEEDINGS{volpin,
AUTHOR = {Essenin Volpin, A.S.},
TITLE = {The ultra-intuitionistic criticism and the
anti-traditional programme for foundations of mathematcs},
BOOKTITLE = {Intuitionism and Proof Theory},
PAGES = {3-45},
YEAR = 1970,
EDITOR = {Kino,A. et al},
PUBLISHER = {North-Holland,Amserdam}
}
@INCOLLECTION{borel-baire,
AUTHOR = {Baire et alii},
TITLE = {Five Letters on Set Theory, 1905},
BOOKTITLE = {From Kant to Hilbert:A Source Book in the Foundations of Mathematics},
PUBLISHER = {Clarendon Press},
YEAR = 1996,
PAGES = {1077--1086},
NOTE = {ISBN 019850537X}
}
@BOOK{ewald96:_from_kant_to_hilber,
EDITOR = {William Ewald},
TITLE = {From Kant to Hilbert:A Source Book in the Foundations of Mathematics},
PUBLISHER = {Clarendon Press},
YEAR = 1996,
NOTE = {ISBN 019850537X}
}
@BOOK{matsuno00,
AUTHOR = {松野孝一郎},
TITLE = {内部観測とは何か},
PUBLISHER = {青土社},
YEAR = 2000,
NOTE = {ISBN 4-7917-5848-X}
}
@BOOK{tada-tomio,
AUTHOR = {多田富男},
TITLE = {免疫の意味論},
PUBLISHER = {青土社},
YEAR = 1993,
NOTE = {ISBN 4791752430}
}
@BOOK{richard89:_comput_comput_funct_logic_and,
AUTHOR = {Richard L. Epstein, Walter A. Carnielli},
TITLE = {Computability, Computable Functions, Logic, and the Foundations of Mathematcs},
PUBLISHER = {Wadsworth \& Brooks/Cole Advanced Books \& Software},
YEAR = 1989,
NOTE = {ISBN 0-534-10356-1}
}
@BOOK{heyting75:_brouw_l,
EDITOR = {A. Heyting},
TITLE = {Brouwer, L.E.J. Collected Works 1. Philosophy and Foundations of Mathematics},
PUBLISHER = {North-Holland},
YEAR = 1975,
ADDRESS = {Amsterdam}
}
@INCOLLECTION{brouwer96:_histor_backg_princ_and_method,
AUTHOR = {J. Brouwer},
TITLE = {Historical Background, principles and methods of intuitionism, 1952},
BOOKTITLE = {From Kant to Hilbert:A Source Book in the Foundations of Mathematics},
EDITOR = {William Ewald},
PUBLISHER = {Clarendon Press},
PAGES = 1197,
YEAR = 1996,
NOTE = {ISBN 019850537X}
}
@MISC{atten03:_luitz_egber_jan_brouw,
AUTHOR = {Mark van Atten},
TITLE = {Luitzen Egbertus Jan Brouwer},
BOOKTITLE = {The Stanford Encyclopedia of Philosophy},
EDITOR = {Edward N. Zalta},
HOWPUBLISHED = {\url{ http://plato.stanford.edu/archives/sum2003/entries/brouwer/}},
YEAR = 2003
}
@ARTICLE{goodstein,
AUTHOR = {R.L. Goodstein},
TITLE = {On the Restricted Ordinal Theorem},
JOURNAL = {Journal of Symbolic Logic},
YEAR = {1944},
VOLUME = {9},
NUMBER = {2},
PAGES = {33-41}
}
@ARTICLE{tsunoda-suurikagaku,
AUTHOR = {角田秀一郎},
TITLE = {数学と複雑系ー数学の未解決問題},
JOURNAL = {数理科学},
YEAR = {2000}
}
@ARTICLE{dummett1975,
AUTHOR = {M.E. Dummett},
TITLE = {Wang's paradox},
JOURNAL = {Synthese},
YEAR = {1975},
VOLUME = {30},
PAGES = {301--324}
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@MISC{sid-paradox,
AUTHOR = {B.Sidney Smith},
TITLE = {Sid's Paradox},
YEAR = 2001,
HOWPUBLISHED = {\url{http://www.mathacademy.com/pr/prime/articles/sid_para/index.asp}}
}
@MISC{sorites-needle,
AUTHOR = {Justin Needle},
TITLE = {Vagueness and the Sorites Paradox - An Evolving Resource},
HOWPUBLISHED = {\url{http://www.btinternet.com/~justin.needle/}},
YEAR = 2003
}
@MISC{sorites-hyde,
AUTHOR = {Dominic Hyde},
TITLE = {Sorites Paradox},
JOURNAL = {Stanford Encyclopedia of Philosophy},
HOWPUBLISHED = {\url{http://plato.stanford.edu/entries/sorites-paradox/}},
YEAR = 1997
}
@ARTICLE{danzig,
AUTHOR = {D. van Danzig},
JOURNAL = {Dialectica},
YEAR = 1956,
VOLUME = 9,
PAGES = {273-277}
}
@INCOLLECTION{danzig89:_is_finit_number,
AUTHOR = {D. van Danzig},
TITLE = {Is $10^{10^{10}}$ a finite number?},
BOOKTITLE = {Computability---Computable functions, Logic, and the Foundation of Mathematics},
PAGES = {258--261},
PUBLISHER = {Pacific Grove},
YEAR = 1989,
EDITOR = {Richard L. Epstein, Walter A. Carnielli},
SERIES = {The Wadsworth \& Brooks/Cole Advanced Books \& Software},
ADDRESS = {California},
NOTE = {ISBN 0-534-10356-1},
ANNOTE = {Originally in Dialectica, vol. 9, pp. 273-277, 1956}
}
@ARTICLE{frog-and-mice,
AUTHOR = {D. van Dalen},
TITLE = {The War of the Frogs and the Mice, or the Crisis of the Mathematische Annalen},
JOURNAL = {Mathematical Intelligencer},
YEAR = {1990},
OPTKEY = {},
OPTVOLUME = {12},
OPTNUMBER = {4},
OPTPAGES = {17--31},
OPTMONTH = {},
OPTNOTE = {},
OPTANNOTE = {}
}
@INPROCEEDINGS{gandy,
AUTHOR = {R.O. Gandy},
TITLE = {Limitations to Mathematical Knowledge},
BOOKTITLE = {Logic Colloquium '80},
PAGES = {129--146},
YEAR = 1982,
EDITOR = {van Dalen,D. et al},
PUBLISHER = {North-Holland}
}
@INCOLLECTION{hilbert1925,
AUTHOR = {David Hilbert},
TITLE = {On the infinite},
BOOKTITLE = {Computability---Computable functions, Logic, and the Foundation of Mathematics},
PAGES = {45--58},
PUBLISHER = {Pacific Grove},
YEAR = 1989,
EDITOR = {Richard L. Epstein, Walter A. Carnielli},
SERIES = {The Wadsworth \& Brooks/Cole Advanced Books \& Software},
ADDRESS = {California},
NOTE = {ISBN 0-534-10356-1},
ANNOTE = {Text of an address delivered June 4, 1925, before a congress of the Westphalian Mathematical Sosciety in M\"unster, in honor of Karl Weierstrass.}
}
@ARTICLE{nelson04:_bookr,
AUTHOR = {Nelson, Edward},
TITLE = {Bookreview:Gnomes in the fog: The reception of Brouwer's intuitionism in the 1920s, by Dennis E. Hesseling, Science Networks --Historical Studies, vol.28 Birkhauer,Base,2003,xxviii + 447 pp.,ISBN 3-7643-6536-6},
JOURNAL = {Bulletin of the AMS},
YEAR = 2004
}
@BOOK{shikata,
AUTHOR = {四方義啓},
TITLE = {大人のためのわかる数学ー数理哲学序説ー},
PUBLISHER = {財団法人国際高等研究所},
YEAR = {1999},
VOLUME = {4},
SERIES = {高等研選書},
ADDRESS = {京都府相楽郡木津町木津川台9丁目3番地、電話0774-73-4000},
NOTE = {ISBN 4-906671-03-9}
}
@BOOK{dummett-int,
AUTHOR = {Dummett, Michael},
TITLE = {Elements of Intuitionism},
PUBLISHER = {Clarendon Press},
PLACE = {Oxford},
YEAR = 2000,
EDITION = {Second},
NOTE = {ISBN 0-19-850524-8}
}
@BOOK{mayberry,
AUTHOR = {Mayberry, J. P.},
TITLE = {The Foundations of Mathematics in the Theory of Sets},
PUBLISHER = {Cambridge University Press},
YEAR = 2000,
NUMBER = 82,
SERIES = {Encyclopedia of Mathematics and its Applications},
ADDRESS = {Cambridge},
NOTE = {ISBN 0-521-77034-3}
}
@ARTICLE{gensei0,
AUTHOR = {郡司ペギオー幸夫},
TITLE = {生命と時間、そして原生-計算と存在論的観測},
JOURNAL = {現代思想},
YEAR = 1994
}
@BOOK{gunji04,
AUTHOR = {郡司ペギオ-幸夫},
TITLE = {原生計算と存在論的観測―生命と時間、そして原生},
PUBLISHER = {東京大学出版会},
YEAR = 2004,
NOTE = {ISBN 4130100971}
}
@BOOK{kripke,
AUTHOR = {ソールA.クリプキ(黒崎宏訳)},
TITLE = {ウィトゲンシュタインのパラドックス-規則・私的言語・他人の心--},
PUBLISHER = {産業図書},
YEAR = 1983,
NOTE = {ISBN 4-7828-0017-7}
}
@BOOK{lavine94:_under_infin,
AUTHOR = {Shaughan Lavine},
TITLE = {Understanding the infinite},
PUBLISHER = {Harvard University Press},
YEAR = 1994,
ADDRESS = {Cambridge, Mass.},
NOTE = {ISBN 0674921178}
}
@ARTICLE{mycielski81:_analy_without_actua_infin,
AUTHOR = {Jan Mycielski},
TITLE = {Analysis without actual infinity},
JOURNAL = {J. Symbolic Logic},
YEAR = 1981,
VOLUME = 46,
PAGES = {625-633}
}
@ARTICLE{mycielski86:_local_finit_theor,
AUTHOR = {Jan Mycielski},
TITLE = {Locally finite theories},
JOURNAL = {J. Symbolic Logic},
YEAR = 1986,
VOLUME = 51,
PAGES = {59-62}
}
@BOOK{nelson,
AUTHOR = {E. Nelson},
TITLE = {Predicative arithmetic},
PUBLISHER = {Princeton University Press},
YEAR = {1987},
NOTE = {ISBN 0-691-08455-6}
}
@BOOK{nelson-nonstandard,
AUTHOR = {E. Nelson},
TITLE = {Radically Elementary Probability Theory},
PUBLISHER = {Princeton University Press},
YEAR = {1987},
SERIES = {Annals of Mathematics Studies},
NUMBER = {117},
NOTE = {ISBN 0-691-08455-6}
}
@BOOK{robinson,
AUTHOR = {Robinson, A.},
TITLE = {Non-Standard Analysis},
PUBLISHER = {North-Holland Publishing Company},
YEAR = {1966}
}
@ARTICLE{r.71:_exist_and_feasib_in_arith,
AUTHOR = {R. Parikh },
TITLE = {Existence and feasibility in arithmetic},
JOURNAL = {Journal of Symbolic Logic},
YEAR = 1971,
VOLUME = 36,
PAGES = {494-508}
}
@BOOK{shoenfield,
AUTHOR = {Shoenfield, Roseph R.},
TITLE = {Mathematical Logic},
PUBLISHER = {Addison-Wesley},
YEAR = 1967,
NOTE = {ISBN 1-56881-1-135-7}
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@INCOLLECTION{sazonov-feasible,
AUTHOR = {Sazonov, Vladimir Yu.},
TITLE = {On feasible numbers},
BOOKTITLE = {Logic and computational complexity},
PAGES = {30-51},
PUBLISHER = {Springer},
YEAR = {1995},
EDITOR = {Leviant D},
VOLUME = {960},
SERIES = {Lecture Notes in computer sicence},
HOWPUBLISHED = {\url{http://www.csc.liv.ac.uk/~sazonov/papers/lcc.ps}}
}
@MISC{sazonov:_feasib_number_how_to_formal,
AUTHOR = {Sazonov, Vladimir Yu.},
TITLE = {On Feasible Numbers (How to Formalise?)},
HOWPUBLISHED = {\url{http://www.csc.liv.ac.uk/~sazonov/papers/lcc-sli.ps}},
YEAR = 1995
}
@BOOK{borel-1952,
AUTHOR = {Borel, Emil},
TITLE = {Les Nombres Inaccessibles},
PUBLISHER = {Gauthier-Villars},
YEAR = {1952}
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@ARTICLE{maclane,
AUTHOR = {Maclane,S.},
TITLE = {The Health of Mahtematics},
JOURNAL = {Inteligentia},
PAGES = {3-8},
YEAR = {1983}
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@BOOK{tanaka-anthology,
EDITOR = {田中一之編},
TITLE = {数学の基礎をめぐる論争--21世紀の数学と数学基礎論のあるべき姿を考える},
PUBLISHER = {シュプリンガーフェアラーク東京},
YEAR = {1999},
NOTE = {ISBN 4-431-70797-2}
}
@BOOK{tanaka1,
AUTHOR = {田中一之},
TITLE = {数学基礎論講義},
PUBLISHER = {日本評論社},
YEAR = {1997},
NOTE = {ISBN 4-535-78241-5}
}
@BOOK{tanaka2,
AUTHOR = {田中一之},
TITLE = {逆数学と二階算術},
PUBLISHER = {河合文化教育研究所},
YEAR = {1997},
NOTE = {ISBN 4-87999-970-9}
}
@BOOK{tanaka3,
AUTHOR = {田中一之},
TITLE = {数の体系と超準モデル},
PUBLISHER = {裳華房},
YEAR = {2002},
NOTE = {ISBN 4-7853-1530-X}
}
@UNPUBLISHED{tsunoda-handai,
AUTHOR = {角田秀一郎},
TITLE = {数学と複雑系},
NOTE = {大阪大学集中講義（理学研究科数学専攻）},
MONTH = {May},
YEAR = 1995
}
@INBOOK{tujisita-seidosha-1998,
AUTHOR = {辻下 徹},
TITLE = {生命と複雑系},
OPTVOLUME = {数学},
SERIES = {複雑系の科学と現代思想},
PUBLISHER = {青土社},
YEAR = {1998},
PAGES = {75-225},
NOTE = {ISBN 4-7917-9145-2}
}
@BOOK{kaneko97,
AUTHOR = {金子邦彦,郡司ペギオ-幸夫,高木由臣},
TITLE = {生命システム},
PUBLISHER = {青土社},
YEAR = 1997,
SERIES = {複雑系の科学と現代思想},
NOTE = {ISBN 4-7917-9141-X}
}
@BOOK{ikeda97,
AUTHOR = {池田研介,津田一郎,松野孝一郎},
TITLE = {カオス},
PUBLISHER = {青土社},
YEAR = 1997,
SERIES = {複雑系の科学と現代思想},
NOTE = {ISBN 4-7917-9143-6}
}
@BOOK{gunji-matsuno97,
AUTHOR = {郡司ペギオ-幸夫,松野孝一郎,オットー・E・レスラー},
TITLE = {内部観測},
PUBLISHER = {青土社},
YEAR = 1997,
SERIES = {複雑系の科学と現代思想},
NOTE = {ISBN 4-7917-9144-4}
}
@ARTICLE{tsujishita2,
AUTHOR = {辻下 徹},
TITLE = {数学と不定性--複雑系の数理・内部観測・生命},
JOURNAL = {現代思想：システムー生命論の未来},
YEAR = 2001,
VOLUME = {29-3},
PAGES = {56--64},
NOTE = {\url{http://ac-net.org/tjst/archives/00futeisei.pdf}}
}
@BOOK{vopenka,
AUTHOR = {Petr Vop$\check{\mbox{e}}$nka},
TITLE = {Mathematics in the Alternative Set Theory},
PUBLISHER = {Teubner},
YEAR = {1979}
}
@BOOK{voppenka72:_theor_of_semis,
AUTHOR = {Petr Vop$\check{\mbox{e}}$nka and Petr H$\acute{\mbox{a}}$jek},
TITLE = {The theory of semisets},
PUBLISHER = {North-Holland},
YEAR = 1972,
VOLUME = 70,
SERIES = {Studies in Logic and the Foundation of Mathematics},
ADDRESS = {Amsterdam},
NOTE = {ISBN 0-7204-2267-1}
}
@BOOK{wit,
AUTHOR = {Wittgenstein,L},
TITLE = {ウィトゲンシュタイン全集},
PUBLISHER = {大修館書店},
YEAR = {1976},
NOTE = {ISBN 4-469-11010-8}
}
@INCOLLECTION{drake,
AUTHOR = {F.R.ドレイク(Drake)},
EDITOR = {田中一之},
KEY = {Drake},
TITLE = {最近の数理論理学と数学の基礎との関係},
BOOKTITLE = {数学の基礎をめぐる論争},
PAGES = {16--37},
PUBLISHER = {シュプリンガー・フェアラーク東京},
YEAR = 1999
}
@INCOLLECTION{Paris.Harrington:77,
AUTHOR = {J. Paris and Leo A. Harrington},
TITLE = {A mathematical incompleteness in Peano Arithmetic},
EDITOR = {Jon Barwise},
BOOKTITLE = {Handbook of Mathematical Logic},
PUBLISHER = {North-Holland},
YEAR = 1977,
PAGES = {1133--1142},
ADDRESS = {Amsterdam}
}
@MISC{tujisita-gakkai,
AUTHOR = {辻下 徹},
TITLE = {数学と複雑システム学の多様な関係},
YEAR = 1998,
HOWPUBLISHED = {\url{http://ac-net.org/tjst/doc/tjst/98X-gakkai.html}}
}
@MISC{tsunoda-sonzaironteki,
AUTHOR = {角田秀一郎},
TITLE = {数学と存在論的観測},
HOWPUBLISHED = {\url{http://altmath.ac-net.org/doc/tsunoda/tsunoda99-2-10.pdf}},
YEAR = 1993,
ANNOTE = {複雑系札幌研究会講演}
}
@ARTICLE{tsunoda-datsukouchiku,
AUTHOR = {角田秀一郎},
TITLE = {数学の脱構築},
JOURNAL = {現代思想},
YEAR = 1999,
PAGES = {258-270}
}
@ARTICLE{tsunoda-science,
AUTHOR = {角田秀一郎},
TITLE = {数学の未解決問題 21世紀に向けて8 -- 数学と複雑系},
JOURNAL = {数理科学},
YEAR = 2000,
VOLUME = 441
}
@MISC{altmath-shushi,
AUTHOR = {辻下 徹},
TITLE = {Altermative Mathematics 談話会 趣旨},
HOWPUBLISHED = {\url{http://altmath.ac-net.org/shushi.php}},
YEAR = 2005
}
@ARTICLE{tsunoda-yuibutsuron,
AUTHOR = {角田秀一郎},
TITLE = {複雑系、内部観測そして数学},
JOURNAL = {季報唯物論研究ー特集「内部観測と複雑系の新地平」},
YEAR = 2002,
VOLUME = 80,
PAGES = {41--50}
}
@ARTICLE{spencer,
AUTHOR = {Spencer, Joel},
TITLE = {Large Numbers and Unprovable Theorems},
JOURNAL = {AMS Monthly},
YEAR = 1983,
VOLUME = 90,
NUMBER = 10,
PAGES = {669-675}
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@ARTICLE{ramsey,
AUTHOR = {F.P.Ramsey},
TITLE = {On a problem of formal logic},
JOURNAL = {Proc. London Math. Soc.},
YEAR = 1930,
PAGES = {264--286}
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@ARTICLE{solovey,
AUTHOR = {J. Ketonen, R. Solovay},
TITLE = {Rapidly growing Ramsey functions},
JOURNAL = {Ann. of Math.},
YEAR = 1981,
VOLUME = 113,
PAGES = {267--314}
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@ARTICLE{friedman,
AUTHOR = {H.V. Friedman},
TITLE = {Finite functions and the necessary use of large cardinals},
JOURNAL = {Annals of Math.},
YEAR = 1998,
VOLUME = 148,
PAGES = {803--893}
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@BOOK{kaye91:_model_of_peano_arithy,
AUTHOR = {Richard Kaye},
TITLE = {Models of Peano Arithmetic},
PUBLISHER = {Clarendon Press},
PLACE = {Oxford},
YEAR = 1991,
NOTE = {ISBN 0-19-853213-X}
}
@INPROCEEDINGS{143685,
AUTHOR = {Klaus Kaiser},
TITLE = {Computations at infinity: a nonstandard approach},
BOOKTITLE = {SAC '92: Proceedings of the 1992 ACM/SIGAPP Symposium on Applied computing},
YEAR = {1992},
ISBN = {0-89791-502-X},
PAGES = {541--546},
LOCATION = {Kansas City, Missouri, United States},
URL = {http://doi.acm.org/10.1145/143559.143685},
PUBLISHER = {ACM Press},
ADDRESS = {New York, NY, USA}
}
@INPROCEEDINGS{isles,
AUTHOR = {David Isles},
TITLE = {Remarks on the Notion of Standard Non-Isomorphic Natural Number Series},
BOOKTITLE = {Constructive Mathematics,Proceedings of the New Mexico State University Conference Held at Las Cruces, New Mexico, August 11--15,1980},
PAGES = {111--134},
YEAR = 1980,
EDITOR = {F.Richman},
VOLUME = 873,
SERIES = {Lecture Notes in Mathematics},
PUBLISHER = {Springer},
NOTE = {Excerpts in Computability---Computable functions, logic, and the foundation of mathematics, by R.L.Epstein et al, pp. 261--268}
}
@ARTICLE{isles92:_what_eviden_is_there_that,
AUTHOR = {D. Isles},
TITLE = {What evidence is there that $2^{65536}$ is a natural number?},
JOURNAL = {Notre Dame Journal of Formal Logic},
YEAR = 1992,
VOLUME = 33,
NUMBER = 4,
PAGES = {465--480}
}
@INPROCEEDINGS{goodman80:_reflec_bishop_philos_of_mathem,
AUTHOR = {Nicolas ~D. Goodman},
TITLE = {Reflections on Bishop's philosophy of mathematics},
BOOKTITLE = {Constructive Mathematics,Proceedings of the New Mexico State University Conference Held at Las Cruces, New Mexico, August 11--15,1980},
PAGES = {135--145},
YEAR = 1980,
EDITOR = {F.Richman},
VOLUME = 873,
SERIES = {Lecture Notes in Mathematics},
PUBLISHER = {Springer},
NOTE = {Reprinted in Computability---Computable functions, logic, and the foundation of mathematics, by R.L.Epstein et al, pp. 254--258}
}
@BOOK{l.a.harrington85:_harvey_fried_resear_found_of_mathem,
EDITOR = {L. A. Harrington and M. D. Morley and A. \check{S}\check{c}edrov and S. G. Simplson},
TITLE = {Harvey Friedman's Research on the Foundations of Mathematics},
PUBLISHER = {North-Holland},
YEAR = 1985,
VOLUME = 117,
SERIES = {Studies in Logic},
ADDRESS = {Amsterdam},
NOTE = {ISBN 0-444-87834-3}
}
@INCOLLECTION{wilkie,
AUTHOR = {Alex Wilkie},
TITLE = {On exponentiation - a solution to Tarski's High School Algebra Problem},
BOOKTITLE = {Connections between Model Theory and Algebraic and Analytic Geometry},
PAGES = {107--129},
YEAR = 2000,
EDITOR = {Angus Macintyre},
VOLUME = 6,
SERIES = {Quaderni di Matematica},
ADDRESS = {Naples},
NOTE = {url:\texttt{ttp://www.maths.ox.ac.uk/~wilkie/on-exp.ps}}
}
@ARTICLE{a.carbone97:_makin_proof_without_modus_ponen,
AUTHOR = {A. Carbone and S. Semmes},
TITLE = {Making proofs without modus ponens:An introduction to the combinatorics and complexity of cut elimination},
JOURNAL = {Bullentin AMS},
KEY = {A. Carbone},
YEAR = 1997,
VOLUME = 34,
NUMBER = 2,
PAGES = {131--159}
}
@ARTICLE{bendegem00:_alter_mathem,
AUTHOR = {Jean Paul van Bendegem},
TITLE = {Alternative Mathematics:The Vague Way},
JOURNAL = {Synthese},
YEAR = 2000,
VOLUME = 125,
PAGES = {19--31}
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@ARTICLE{mycielski:_tension_between_tarsk_nomin_and,
AUTHOR = {Jan Mycielski},
TITLE = {On the tension between Tarski's nominamism and his model theory (Definitions for a mathematical model of knowledge)},
JOURNAL = {Annals of Pure and Applied Logic},
VOLUME = 126,
YEAR = 2004,
PAGES = {215--224},
URL = {http://spot.colorado.edu/~jmyciel/Tarski.ps}
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@MISC{tragesser98:_part_i,
AUTHOR = {Robert Tragesser},
TITLE = {Part I:Ultrafinitism,Naturalism,Vagueness},
HOWPUBLISHED = {\url{http://www.cs.nyu.edu/pipermail/fom/1998-April/001825.html}},
MONTH = 4,
YEAR = 1998
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@INPROCEEDINGS{cardone94:_stric_finit_and_feasib,
AUTHOR = {Felice Cardone},
TITLE = {Strict Finitism and Feasibility},
BOOKTITLE = {Logic and Computational Complexity,International Workshop LCC '94, Indianapolis, IN, USA, October 13-16,1994},
PAGES = {1--21},
YEAR = 1994,
EDITOR = {Daniel Leviant},
VOLUME = 960,
SERIES = {Lecture notes in computer science}
}
@ARTICLE{p.k.rashevskii73:_dogma_of_natur_number,
AUTHOR = {P.K.Ra\check{s}evski\check{i}},
TITLE = {On the dogma of natural numbers},
JOURNAL = {Russian Mathematical Surveys},
YEAR = 1973,
VOLUME = 28,
NUMBER = 4,
PAGES = {143--148}
}
@INCOLLECTION{p.bernays64:_platon_in_mathem,
AUTHOR = {P. Bernays},
TITLE = {On Platonism in Mathematics},
PUBLISHER = {Cambridge University Press},
YEAR = 1983,
BOOKTITLE = {P.Benacerraf and H.Putnam, editors, Philosophy of Mathematics},
ADDRESS = {Cambridge},
EDITION = {second},
PAGES = {258--272},
NOTE = {Originally appeared in Frech in L'Enseignement Mathematique,1935,pp.52-69}
}
@BOOK{buss86:_bound_arith,
AUTHOR = {S.R. Buss},
TITLE = {Bounded Arithmetic},
YEAR = 1986,
PUBLISHER = {Bibliopolis},
NOTE = {Revision of 1985 Princeton University Ph.D. thesis }
}
@ARTICLE{buss99:_bound_arith_proof_compl_and,
AUTHOR = {Samuel R. Buss},
TITLE = {Bounded arithmetic, proof complexity and two papers of Parikh},
JOURNAL = {Annals of Pure and Applied Logic},
YEAR = 1999,
VOLUME = 96,
PAGES = {43--55}
}
@ARTICLE{lifschitz79:_intuit_defin_of_class_natur_number,
AUTHOR = {Vladimir Lifschitz},
TITLE = {An Intuitionistic Definition of Classical Natural Numbers},
JOURNAL = {Proc. AMS},
YEAR = 1979,
VOLUME = 77,
NUMBER = 3,
PAGES = {385--388}
}
@ARTICLE{lifschitz82:_const_asser_in_exten_of_class_mathem,
AUTHOR = {Vladimir Lifschitz},
TITLE = {Constructive Assertions in an Extension of Classical Mathematics},
JOURNAL = {Journal of Symbolic Logic},
YEAR = 1982,
VOLUME = 47,
NUMBER = 2,
PAGES = {359--387}
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@ARTICLE{martin92:_unprov_ramsey_type_theor,
AUTHOR = {Martin Loebl, Jaroslav Ne\check{s}et\check{r}il},
TITLE = {An unprovable Ramsey-type theorym},
JOURNAL = {Proc AMS},
YEAR = 1992,
VOLUME = 116,
NUMBER = 3,
PAGES = {819--824}
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@ARTICLE{smoryhecknski79:_some_rapid_growin_funct,
AUTHOR = {Craig Smory$\check{\mbox{n}}$ski},
TITLE = {Some rapidly growing functions},
JOURNAL = {Math. Intelligencer},
YEAR = 1979,
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NUMBER = 3,
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@BOOK{gunji02,
AUTHOR = {郡司 ペギオ-幸夫},
TITLE = {生命理論I 生成する生命 },
PUBLISHER = {哲学書房},
YEAR = 2002,
VOLUME = 6,
SERIES = {哲学文庫},
NOTE = {ISBN 4-88679-080-1}
}
@BOOK{mannoury09:_method_und_philos_zur_elemen,
AUTHOR = {G. Mannoury},
TITLE = {Methodologisches und Philosophisches zur Elementarmathematik},
PUBLISHER = {P.Visser},
YEAR = 1909,
ADDRESS = {Haarlem},
ANNOTE = {Referred by D. van Dantzig in "Is $10^{10^{10}}$ a finite number?" }
}
@BOOK{marion98:_wittg_finit_and_found_of_mathem,
AUTHOR = {Mathieu Marion},
TITLE = {Wittgenstein, Finitism, and the Foundations of Mathematics},
PUBLISHER = {Clarendon Press},
YEAR = 1998,
SERIES = {Oxford Philosophical Monographs},
NOTE = {ISBN 0-19-823516-X}
}
@INCOLLECTION{matt98:_hierar_of_provab_recur_funct,
AUTHOR = {Matt Fairtlough, Stanley S. Wainer},
TITLE = {Hierarchives of Provably Recursive Functions},
BOOKTITLE = {Handbook of Proof Theory},
PAGES = {149--207},
PUBLISHER = {Elsevier},
YEAR = 1998,
EDITOR = {Samuel R. Buss},
VOLUME = 137,
SERIES = {Studies in Logic and the Foundation of Mathematics},
CHAPTER = {III},
ADDRESS = {Amsterdam},
NOTE = {ISBN 0-444-89840-9}
}
@BOOK{buss98:_handb_of_proof_theor,
EDITOR = {Samuel R. Buss},
TITLE = {Handbook of Proof Theory},
PUBLISHER = {Elsevier},
YEAR = 1998,
VOLUME = 137,
SERIES = {Studies in Logic and the Foundation of Mathematics},
ADDRESS = {Amsterdam},
NOTE = {ISBN 0-444-89840-9}
}
@ARTICLE{beck80:_relat_between_algeb_and_analy,
AUTHOR = {Jon M. Beck},
TITLE = {On the relationship between algebra and analysis},
JOURNAL = {Journal of Pure and Applied Algebra},
YEAR = 1980,
VOLUME = 19,
PAGES = {43--60}
}
@INCOLLECTION{beck79:_simpl_sets_and_found_of_analy,
AUTHOR = {Jon M. Beck},
TITLE = {Simplicial sets and the foundations of analysis},
BOOKTITLE = {Proceedings of Conference on Sheaf Theory,Durham,England(July 1977)},
PAGES = {113--124},
PUBLISHER = {Springer},
YEAR = 1979,
VOLUME = 753,
SERIES = {Lecture Notes in mathematics},
ADDRESS = {Berlin}
}
@ARTICLE{richman96:_inter_with_const_mathem,
AUTHOR = {Fred Richman},
TITLE = {Interview with a constructive mathematician },
JOURNAL = {Modern Logic},
YEAR = 1996,
VOLUME = 6,
PAGES = {247--271},
NOTE = {\url{http://www.math.fau.edu/Richman/Docs/intrview.html}}
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@BOOK{takeuchi-95,
AUTHOR = {竹内外史},
TITLE = {証明論と計算量},
PUBLISHER = {裳華房},
YEAR = 1995,
ADDRESS = {東京},
NOTE = {ISBN 4-7853-1096-0}
}
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AUTHOR = {John von Neumann},
TITLE = {Eine Axiomatisierung der Mengenlehre},
JOURNAL = {Journal fur die reine und angewandte Mathematik},
YEAR = 1925,
VOLUME = 154,
NUMBER = {219-240},
NOTE = {Reprinted as pp. 34--56 in collected works}
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@ARTICLE{neumann27:_zur_hilber_beweis,
AUTHOR = {John von Neumann},
TITLE = {Zur Hilbertischen Beweistheorie},
JOURNAL = {Math. Zschr. },
YEAR = 1927,
VOLUME = 26,
NUMBER = {1--46},
NOTE = {Reprinted as pp. 256--300 in collected works, Vol.1}
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AUTHOR = {H.-D. Ebbinghaus and J. Flum },
TITLE = {Finite Model Theory},
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PUBLISHER = {Springer},
YEAR = 1999,
NOTE = {ISBN 3-540-65758-4}
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AUTHOR = {R.~L. Graham and B.~L. Rothschild and J.~H. Spencer},
TITLE = {Ramsey Theory},
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YEAR = 1980
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EDITOR = {Gila Sher and Richard Tieszen},
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NOTE = {ISBN: 0521650763}
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@BOOK{boolos98:_logic_logic_and_logic,
AUTHOR = {George Boolos},
TITLE = {Logic, Logic, and Logic},
PUBLISHER = {Harvard University Press},
YEAR = 1998,
ADDRESS = {London},
NOTE = {ISBN 0-674-53767-X}
}
@INCOLLECTION{boolos98:_must_we_believ_in_set_theor,
AUTHOR = {George Boolos},
TITLE = {Must we believe in set theory?},
EDITOR = {Richard Jeffrey},
BOOKTITLE = {Logic,Logic, and Logic},
PAGES = {120--132},
PUBLISHER = {Harvard University Press},
YEAR = 1998,
ADDRESS = {London},
NOTE = {ISBN 0-674-53767-X}
}
@INCOLLECTION{boolos98:_zoomin_down_slipp_slope,
AUTHOR = {George Boolos},
TITLE = {Zooming down the slippery slope},
BOOKTITLE = {Logic,Logic, and Logic},
PAGES = {354--364},
PUBLISHER = {Harvard University Press},
YEAR = 1998,
ADDRESS = {London},
NOTE = {ISBN 0-674-53767-X},
EDITOR = {Richard Jeffrey}
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@INCOLLECTION{boolos98:_curious_infer,
AUTHOR = {George Boolos},
TITLE = {A curious inference},
BOOKTITLE = {Logic,Logic, and Logic},
PAGES = {376--382},
PUBLISHER = {Harvard University Press},
YEAR = 1998,
ADDRESS = {London},
NOTE = {ISBN 0-674-53767-X},
EDITOR = {Richard Jeffrey}
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AUTHOR = {Alonzo Church},
TITLE = {Introduction to Mathematical Logic},
PUBLISHER = {Princeton University Press},
YEAR = 1956,
VOLUME = {I},
ADDRESS = {Princeton,New Jersey},
NOTE = {ISBN 0-691-07984-6}
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AUTHOR = {Ren\'e Lavendhomme},
TITLE = {Basic Concepts of Synthetic Differential Geometry},
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SERIES = {Kluwer Texts in the Mathematical Sciences},
ADDRESS = {Dordrecht},
NOTE = {ISBN 0-7923-3941-X}
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@BOOK{moerdijk91:_model_for_smoot_infin_analy,
AUTHOR = {Ieke Moerdijk and Gonzalo E. Reyes},
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@BOOK{mortensen95:_incon_mathemd,
AUTHOR = {Chris Mortensen},
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VOLUME = 312,
SERIES = {Mathematics and Its Applications},
NOTE = {ISBN 0-7923-3186-9}
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AUTHOR = {L. Henkin},
TITLE = {On mathematical induction},
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PAGES = {323--338},
ANNOTE = {cited by Cardone}
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ANNOTE = {cited by Cardone}
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PAGES = {391--420},
ANNOTE = {cited by Cardone}
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AUTHOR = {J. Simon},
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EDITOR = {H.J. Skala and S. Termini and E. Trillas},
ADDRESS = {Dordrecht}
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@BOOK{lawvere91:_concep_mathem_first_introd_to_categ,
AUTHOR = {F. William Lawvere and Stephen H. Schanuel},
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YEAR = 1991,
ADDRESS = {Buffalo, NY},
NOTE = {ISBN 0-9631805-1-7}
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AUTHOR = {S. Shapiro},
TITLE = {primer on vagueness},
HOWPUBLISHED = {\url{http://www.cs.nyu.edu/pipermail/fom/2005-may/008956.html}},
MONTH = {May},
YEAR = 2005
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AUTHOR = {Pavel Pudl\'ak},
TITLE = {The Lengths of Proofs},
BOOKTITLE = {Handbook of Proof THeory},
PAGES = {547--637},
PUBLISHER = {Elsevier},
YEAR = 1998,
EDITOR = {Samuel R. Buss},
VOLUME = 137,
SERIES = {Studies in Logic and the Foundations of Mathematics},
CHAPTER = {VIII},
ADDRESS = {Amsterdam},
NOTE = {ISBN 0-444-89840-9}
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AUTHOR = {R. Parikh},
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JOURNAL = {Transactions of the American Mathematical Society},
YEAR = 1973,
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PAGES = {29--36}
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YEAR = 1994,
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PAGES = {737--756}
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AUTHOR = {A.W.ム−ア（石村多門訳）},
TITLE = {無限−その哲学と数学},
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NOTE = {ISBN 4-501-61490-0}
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AUTHOR = {A.W. Moore},
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ANNOTE = {First edition, 1990}
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AUTHOR = {J. J. O'Connor and E. F. Robertson},
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HOWPUBLISHED = {\url{http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Cantor.html}},
YEAR = 1998
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AUTHOR = {ソール・A.クリプキ , 黒崎 宏訳},
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AUTHOR = {Jaroslav Ne$\check{\mbox{s}}$et$\check{\mbox{r}}$il},
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BOOKTITLE = {Handbook of Combinatorics},
PAGES = {1331-1403},
EDITOR = {R. Graham, M. Gr$\ddot{\mbox{o}}$tschel and L. },
VOLUME = 2,
CHAPTER = 25,
NOTE = {ISBN 4-501-61490-0}
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@BOOK{maclane98:_categ_for_workin_mathem,
AUTHOR = {S. Maclane},
TITLE = {Categories for the Working Mathematician},
PUBLISHER = {Springer},
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EDITION = {2nd},
NOTE = {ISBN 0-387-98403-8}
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AUTHOR = {F.W. Lawvere},
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YEAR = 1992,
ADDRESS = {Berlin},
NOTE = {ISBN 0-387-97710-4}
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AUTHOR = {辻下徹},
TITLE = {複雑系の数理--高次元圏論への招待},
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YEAR = 1998
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AUTHOR = {John C. Baez and James Dolan},
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AUTHOR = {辻下 徹},
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AUTHOR = {C.C. Chang and H. Jerome Keisler},
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AUTHOR = {林 晋},
TITLE = {ヒルベルトと20世紀数学ー公理主義とは何だったか？},
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AUTHOR = {黒川信重},
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AUTHOR = {D. Mumford},
TITLE = {The Dawning of the Age of Stochasticity},
BOOKTITLE = {Mathematics:Frontiers and Perspectives},
PAGES = {197--218},
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YEAR = 1999,
EDITOR = {V. Arnold et al},
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AUTHOR = {M. Davis and Y. Matijasevi$\check{\mbox{c}}$ and J. Robinson},
TITLE = {Hilbert's tenth problem. Diophantine equations: Positive Aspects of a negative solution},
BOOKTITLE = {Mathematical developments arising from Hilbert problems},
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ADDRESS = {Providence}
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EDITOR = {黒木 玄},
TITLE = {黒木のなんでも掲示板3},
KEY = {黒木},
MONTH = 3,
YEAR = 2000,
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AUTHOR = {J.E. リトルウッド},
TITLE = {大きな数},
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BOOKTITLE = {リトルウッドの数学スクランブル},
PUBLISHER = {近代科学社},
EDITOR = {B.ボロバシュ編、金光滋訳},
NOTE = {ISBN4-7649-1016-0}
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@MISC{simpson:_mailin_list,
EDITOR = {S. Simpson et al},
TITLE = {Mailing List: FOM -- Foundations of Mathematics},
KEY = {S. Simpson},
HOWPUBLISHED = {\url{http://www.cs.nyu.edu/pipermail/fom/}},
YEAR = 1997
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AUTHOR = {W. Lawvere},
TITLE = {Diagonal Arguments and Cartesian Closed Categories},
BOOKTITLE = {Category theory, homology theory and their applications : proceedings of the conference held at the Seattle Research Center of the Battelle Memorial Institute, June 24-July 19, 1968},
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EDITOR = {Jean van Heijenoort},
TITLE = {From Frege to G\u{o}del -- A Source Book in Mathematical Logic, 1879--1931},
PUBLISHER = {Harvard University Press},
YEAR = 1967,
ADDRESS = {Cambridge},
NOTE = {ISBN 0-674-32449-8}
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@BOOK{marker02:_model_theor,
AUTHOR = {D. Marker},
TITLE = {Model Theory:An Introduction},
PUBLISHER = {Springer},
YEAR = 2002,
VOLUME = 217,
SERIES = {Graduate Texts in Mathematics},
ADDRESS = {Berlin},
NOTE = {ISBN 0-387-98760-6}
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@BOOK{krajiheckek95:_bound_arith_propos_logic_and_compl_theor,
AUTHOR = {Jan Kraj\'i$\check{\mbox{c}}$ek},
TITLE = {Bounded Arithmetic, Propositional Logic, and Complexity Theory},
PUBLISHER = {Cambridge University Press},
YEAR = 1995,
VOLUME = 60,
SERIES = {Encyclopedia of Mathematics and its applications},
ADDRESS = {Cambridge},
NOTE = {ISBN 0-521-45205-8}
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@ARTICLE{feferman99:_does_mathem_need_new_axiom,
AUTHOR = {Solomon Feferman},
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@BOOK{benacerraf83:_philos_of_mathem_selec_readin,
EDITOR = {P. Benacerraf and H. Putnam},
PUBLISHER = {Cambridge University Press},
YEAR = 1983,
TITLE = {Philosophy of Mathematics, Selected readings},
ADDRESS = {Cambridge},
EDITION = {second},
NOTE = {ISBN 0-521-29648-X}
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@ARTICLE{cichon83:_short_proof_of_two_recen,
AUTHOR = {E.A. Cichon},
TITLE = {A short proof of two recently discovered independence results unsing recursion theoretic methods},
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PAGES = {704--706}
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