@inproceedings{Lakatos,
author = {Imre Lakatos},
year = {1970},
title = {History of science and its rational reconstructions},
booktitle = {\textit{Proceedings of the Biennial Meeting of Philosophy of Science Association}},
publisher = {Springer},
address	= {New York},
pages = {91-136},
}

@incollection{Wigner,  
author = {Wigner, Eugene},
year = {1967},
title = {The unreasonable effectiveness of mathematics in the natural sciences},
booktitle = {\textit{Symmetries and reflections}},
publisher = {Indiana Univ. Press},
address	= {Indiana},
pages= {222},
}

@book{Heath,
author = {Heath, Thomas L},
year = {1926},
title = {\textit{The Thirteen Book of Euclid's Elements}},
edition = {second},  
note = {Translated from the Greek text of Heiberg. Book X-XIII}, 
publisher = {Cambridge University Press},
address	= {Cambridge},
}

@article{Cantor2,
author = {Cantor, Georg},
year = {1879},
title = {\"{U}ber die unendliche lineare Punktmannigfalltigkeiten}, journal = {\textit{Mathematischen Annalen,}},
volume = {15},
pages = {1-7},
note = {Georg Cantor, Abhandlungen Mathematischen und Philosophischen Inhalts, ed. Ernst Zermelo, 1932, Reprinted by Georg Olms, Hildesheim, 1966},
}

@book{Poincar1,
author = {Poincar\'{e}, Henri},
year = {1902},
title = {\textit{La science et l'hypoth\`{e}se}},
publisher = {Flammarion},
address	= {Paris},
note = {English translation by W. J. G. Science and Hypothesis, W. Scott, London, 1905, Reprinted by Dover, New York, 1952},
}

@book{Poincar2,
author = {Poincar\'{e}, Henri},
year = {1908},
title = {\textit{Science et m\'{e}thode}},
publisher = {Flammarion},
address	= {Paris},
}

@book{Galilei,
author = {Galilei, Galileo},
year = {1638},
title = {\textit{Discorsi e Dimostrazioni Matematiche, intorno a due nuoue Scienze Attenenti alla Mecanica i Movimenti Locali}}, 
publisher = {Appresso Elsevirii},
address	= {Leiden},
note = {English translation by Henry Crew and Alfonso de Salvo, Dialogues Concerning Two New Sciences, Macmillan, 1914, Reprinted by Dover, New York 1954},  
}

@article{Russel,
author = {Russel, Bertrand},
year = {1908},
title = {Mathematical logic as based on the theory of types},
journal = {\textit{American Journal of  Mathematics}},
volume = {30},
pages = {222-262},
note = {From Frege to G\"{o}del, edi.J. v. Heijenoort, Harvard University Press, 1967, 150-182},
}

@article{Goedel,
author = {G\"{o}del, Kurt},
year = {1931},
title = {\"{U}ber formel unentscheidbare S\"{a}tz der Principia Mathematica und verwandter System I},
journal = {\textit{Monatschefte f\"{u}r Mathematik und Physik}}, 
volume = {38},
pages = {173-198},
note = {Kurt G\"{o}del collected works, Vol.1, ed. S. Feferman, 
Oxford University Press, New York, 1986}, 
}

@book{Weyl,
author = {Weyl, Hermann},
year = {1949},
title = {\textit{Philosophy of Mathematics and Natural Science. Appendix A: The structure of Mathematics}},
note = {English edition based on a translation by Olaf Helmer, Princeton University Press},
address	= {New Jersey}
}

@incollection{Dieudonn,
author = {Dieudonn\'{e}, Jean},
year = {1982},
title = {Math\'{e}matiques vides et math\'{e}matiques significatives},
booktitle = {\textit{Penser les math\'{e}matiques, S\'{e}minaire de philosophie et math\'{e}matiques de l'\'{E}cole normale sup\'{e}rieure}}, 
publisher = {\'{E}ditions du Seuil},
address	= {Paris},
}

@article{Hilbert,
author = {Hilbert, David},
year = {1926},
title = {\"{U}ber das Unendliche}, 
journal = {\textit{Mathematischen Annalen}},
volume = {95},
pages = {161-190}, 
note = {English translation by Jean van Heijenoort, From Frege to  G\"{o}del, Harvard University Press, Massachusetts, 1967, 367-392},
}

@inproceedings{Robinson,
author = {Robinson, Abraham},
year = {1979},
title = {Concerning progress in the philosophy of mathematics},
booktitle = {\textit{Selected Papers of Abraham Robinson volume 2, Nonstandard Analysis and Philosophy}},
editor = {W. A. J. Luxemburg},
publisher = {Yale University Press},
address	= {New Haven},
pages = {556-567},
}

@book{Dedekind,
author = {Dedekind, Julius W. R},
year = {1872},
title = {\textit{Stetigkeit und Irrationale Zahlen}},  
publisher = {Friedr. Vieweg},
address	= {Brawnschweig},
}

@incollection{Newton1,
author = {Newton, Isaac},
year = {1666},
title = {The October 1666 Tract on Fluxions},
booktitle = {\textit{Mathematical Papers of Isaac Newton}}, 
volume = {1},
editor = {D. T. Whiteside},
publisher = {Cambridge University Press, 1967},
address	= {New York},
pages = {400-448},
}

@incollection{Newton2,
author = {Newton, Isaac},
year = {1670},
title = {The Tract 'de Methodis Serierum et Fluxionum',winter 1670-1671, with English translation, A treatise of the methods of series and fluxions},
booktitle = {\textit{The Mathematical Papers of Isaac Newton}},
volume = {3},
editor = {D. T. Whiteside}, 
publisher = {Cambridge University Press, 1969}, 
address	= {New York},
pages = {32-117},
}

@book{Arnol'd,
author = {Arnol'd, Vladimir I},
year = {1989},
title = {\textit{Gyuigens i Barru, N'yuton, i Guk}},
note = {in Russian, English translation by Eric J. F. Primrose,  Huygens and Barrow, Newton and Hooke, Birkh\"{a}user, Basel, 1990},
publisher = {Nauka FML},
address	= {Moscow},
}

@book{Diels,
author = {Diels, Hermann},
year = {1961},
title = {\textit{Die Fragmente der Vorsokratiker}},
volume = {1},
note = {Zenon, B. Fragmente},
publisher = {Weidmannsche},
address	= {Berlin},
pages = {255-258},
}

@book{Berkeley,
author = {Berkeley, George},
year = {1734},
title = {\textit{The Analyst, or, A Discourse Addressed to an Infidel Mathematician}},
publisher = {Jacob Tonson},
address	= {London},
note = {Reprinted in  From Kant to Hilbert, 1, ed W. B. Ewald, Oxford Science Publications, New York, 1996, 60-92},
}

@book{Cauchy2,
author = {Cauchy, Augustin L},
year = {1823},
title = {\textit{R\'{e}sum\'{e} des Le\c{c}on Donn\'{e}es a l'\'{E}cole Royale Polytechnique, sur le Calcule Infinit\'{e}simal}},  
publisher = {L'imprimerie Royale},
address	= {Paris},
}

@book{Cauchy1,
author = {Cauchy, Augustin L},
year = {1821},
title = {\textit{Cours d'Analyse de l'\'{E}cole royale Polytechnique, 1 Partie. Analyse Alg\'{e}brique}},  
publisher = {L'imprimerie Royale},
address	= {Paris},
note = {English translation by Robert E. Bradley, C. Edward Sandifer,  Cauchy's Cours d'Analyse, Springer, New York, 2009},
}

@book{Klein,
author = {Klein, Felix},
year = {1924},
title = {\textit{Elementarmathematik vom H\"{o}heren Standpunkte aus, 3rd ed.}},
volume = {I}, 
publisher = {Springer},  
address	= {Berlin},
note = {English translation by E. R. Hedrik and C. A. Noble, Elementary Mathematics from Advanced Standpoint, Arithmetic, Algebra, Analysis, Dover, New York, 2004},
}

@book{Bourbaki,
author = {Bourbaki, Nicolas},
year = {1969},
title = {\textit{\'{E}l\'{e}ments d'histoir des math\'{e}matiques}},
publisher = {Hermann},
address	= {Paris},
note = {English translation by J. Meldrum, Elements of the history of Mathematics, Springer, Berlin, 1994},
}


@book{Belhoste,
author = {Belhoste, Bruno},
year = {1985},
title = {\textit{Cauchy, 1789-1857. Un math\'{e}maticien l\'{e}gitimiste au XIXe si\`{e}cle}},
publisher = {Belin},
address	= {Paris},
}

@incollection{Friedman,
author = {Friedman, Harvey},
year = {1974},
title = {Some systems of second order arithmetic and their use},
booktitle = {\textit{Proceedings of International Congress of Mathematicians}},
publisher = {Canadian Mathematical Congress},
address	= {Canada},
pages = {235-242},
}

@article{Simpson1,
author = {Simpson, Stephen G},
year = {1988},
title = {Partial realization of Hilbert's program},
journal = {\textit{Journal of Symbolic Logic}},
volume = {53}, 
pages = {349-363},
}

@article{Riemann,
author = {Riemann, Bernhart},
year = {1854},
title = {\"{U}ber die Darstellbarbkeit einer Function durch einer trigonometrische Reihe}, 
journal = {\textit{Abhandlungen der K\"{o}niglichen Gesellschaft der Wissenschaften zu G\"{o}ttingen}},
volume = {13},
note = {English translation by R. Baker and others, On the representation of a function by a trigonometric series, Collected Papers Bernhart Riemann, Kendrick Press, Herber City, 2004},
}

@book{Fourier,
author = {Fourier, Jean B. J},
year = {1822},
title = {\textit{Th\'{e}orie Analytique de la Chaluer}}, 
publisher = {Firnin Diot},
address	= {Paris},
note = {English translation by Alexander Freeman, Analytical Theory of Heat, Cambridge University Press, New York, 1878, reprinted 2009},
}

@book{Kondo,
author = {Kondo, Youitsu},
year = {1947},
title = {\textit{Suugaku shisoushi Josetsu(Introduction to the history of mathematical thought)}},
note = {in Japanese, in Kondo Yoitsu Suugakushi Chosakushuu (Collected Works of Yoitsu Kondo on History of Mathematics), 2, ed. C. Sasaki, Nihon Hyouron Sha, Tokyo, 1994},
publisher = {San-ichi Shobo},
address	= {Tokyo},
}

@book{Bottazzini,
author = {Bottazzini, Umberto},
year = {1981},
title = {\textit{Il Calcolo Sublime: Storia dell'Analisi Matematica da Euler a Weierstrass}}, 
publisher = {Torino},
note = {English translation by Warrn Van Egmond, The higher calculus: a history of real and complex analysis from Euler to Weierstrass},  
publisher = {Springer, 1986},
address	= {New York},
}

@article{Cantor1,
author = {Cantor, Georg},
year = {1872},
title = {\"{U}ber die Ausdehnung eines Satzes aus der Theorie der trigonometrischen Reihen},
journal = {\textit{Mathematischen Annalen}}, 
volume = {5},
pages = {123-132},
note = {Georg Cantor, Abhandlungen Mathematischen und Philosophischen Inhalts, ed. Ernst Zermelo, 1932, Reprinted by Georg Olms, Hildesheim, 1966},
}

@article{Gentzen1,
author = {Gentzen, Gerhard},
year = {1936},
title = {Die Widerspruchsfreiheit der reinen Zahlentheorie},
journal = {\textit{Mathematischen Annalen,}},
volume = {112},
pages = {493-565},
}

@article{Gentzen2,
author = {Gentzen, Gerhard},
year = {1936},
title = {Der Unendlichkeitsbegriff in Mathematik}, 
journal = {\textit{Semester-Berichte, M\"{u}nster in/w, 9th Semester, Winter 1936-37}}, 
pages = {65-80},
}

@article{Cantor4,
author = {Cantor, Georg},
year = {1895}, 
title = { Beitr\"{a}ge zur Begr\"{u}ndung der transfiniten Mengenlehre},
journal = {\textit{Mathematischen Annalen}},  
volume = {46},
pages = {481-512},
note = {also 49, 207-246, Georg Cantor, Abhandlungen Mathematischen und Philosophischen Inhalts, ed. Ernst Zermelo, 1932, Reprinted by Georg Olms, Hildesheim, 1966},
}

@book{Tanaka,
author = {Tanaka, Kazuyuki},
year = {1997},
title = {\textit{Gyakusuugaku to Nikai Sanjutsu (Reverse Mathematics and Second Order Arithmetic)}},
note = {in Japanese},
publisher = {Kawai Shuppan},
address	= {Tokyo},
}

@book{Helmholtz,
author = {Helmholtz, Hermann von},
year = {1847},
title = {\textit{\"{U}ber die Erhaltung der Kraft, eine Physikalische Abhandlung}},
publisher = {G. Reimer},
address	= {Berlin},
}

@article{Michelson,
author = {Michelson, Albert Abraham and Morley, Edward Williams},
year = {1887},
title = {On the Relative Motion of the Earth and the Luminiferous Ether},
journal = {\textit{American Journal of Science, Series 3}},
volume = {34},
pages = {333-345},
}

@book{Faraday,
author = {Faraday, Michael},
year = {1839},
title = {\textit{Experimental Researches in Electricity}},
volume = {1-3}, 
publisher = {Richard and J. E. Taylor, 1839-1855},
address	= {London},
}

@book{Maxwell,
author = {Maxwell, James C},
year = {1873},
title = {\textit{A Treatise on  Electricity and Magnetism}},
publisher = {Constable},
address	= {London}, 
note = {Reprinted by Dover, New York, 1954}
}

@incollection{Einstein2,
author = {Einstein, Albert},
year = {1931},
title = {Maxwell's influence on the development of the conception of physical reality},
booktitle = {\textit{James Clark Maxwell: A Commemoration}}, 
publisher = {Cambridge University Press},
address	= {Cambridge, England},
pages = {66-73},
note = {In this quotation, only once the word 'partial' was replaced to 'ordinary' according to 1939 German version)},
}


@book{Cohen,
author = {Cohen, Paul J},
year = {1966},
title = {\textit{Set Theory and the Continuum Hypothesis}},
publisher = {W. A. Benjamin},
address	= {New York}, 
}

@article{Kunen,
author = {Kunen, Kenneth},
year = {1971},
title = {Elementary embeddings and infinitary combinatorics},
journal = {\textit{Journal of Symbolic Logic}},
volume = {36},
pages = {407-413},
}

@article{Einstein1,
author = {Einstein, Albert},
year = {1905},
title = {Zur Elektrodynamik bewegter K\"{o}rper},
journal = {\textit{Annalen der Physik}},
volume = {17},
pages = {891-921},
note = {English translation by Anna Beck, On the electrodynamics of moving bodies, The collected papers of Albert Einstein, 2, Princeton University Press, New Jersey, 1989},
}

@article{Voigt,
author = {Voigt, Woldemar},
year = {1887},
title = {\"{U}ber das Doppler'sche Princip},
journal = {\textit{Nachrichten von Gesellschaft der Wissenschaften zu G\"{o}ttingen}},
volume = {8},
pages = {41-51},
}

@article{Planck,
author = {Planck, Max},
title = {'\"{U}ber das Gesetz der Eneregieverteilung im Normalspectrum},
journal = {\textit{Annalen der Physik}},
volume = {309},
year = {1901},
pages = {553-563},
}

@article{Bohr1,
author = {Bohr, Niels},
year = {1913},
title = {On the constitution of atoms and molecules},
journal = {\textit{Philosophical Magazine}}, 
volume = {26},
pages = {1-26},
}

@book{Broglie,
author = {Broglie, Louis de},
year = {1937},
title = {\textit{Mati\`{e}re et Lumi\`{e}re}},
publisher = {Albin Michel},
address	= {Paris},
note = {English translation by W. H. Johnston, Matter and Light; the New Physics, Dover, New York, 1939}, 
}

@article{Bohr2,
author = {Bohr, Niels},
year = {1929},
title = {Wirkungusquantum und Naturbeschreibung},
journal = {\textit{Die Naturwissenschaften}},
volume = {17},
pages = {483},
note = {English translation Quantum of action and the description of nature, in Atomic Theory and Description of Nature, Cambridge University Press, 1934},
}

@book{Dirac1,
author = {Dirac, Paul A. M},
year = {1930},
title = {\textit{The Principles of Quantum Mechanics}}, 
publisher = {Oxford, Clarendon Press},
address�= {London},
}

@book{Neumann,
author = {Neumann, Johann v},
year = {1932},
title = {\textit{Die Mathematische Grundlagen der Quantenmechanik}},
publisher = {Springer},
address	= {Berlin},
}

@incollection{Yukawa,
author = {Yukawa, Hideki},
year = {1957},
note = {Foreword},
booktitle = {\textit{Ryoushi Rikigaku no Suugakuteki Kiso (Japanese translation of  Johann v. Neumann, Die Mathematische Grundlagen der Quantenmechanik}},  
publisher = {Misuzu Shobou},
address	= {Tokyo},
}

@book{Lighthill,
author = {Lighthill, Michael J},
year = {1958},
title = {\textit{An Introduction to Fourier Analysis and Generalized Functions}},
publisher = {Cambridge Univsersity Press},
address	= {England},
}

@book{Feynman,
author = {Feynman, Richard P. and Hibbs, Albert R},
year = {1965},
title = {\textit{Quantum Mechanics and Path Integrals}},
publisher = {McGraw-Hill},
address	= {New York},
}

@article{Nambu,
author = {Nambu, Yoichiro},
year = {1984},
title = {What are the possibilities for extending our understanding of elementary particles and their interactions to much greater energies? Concluding remarks,18th Solvay Conference, Higher energy physics.}, 
journal = {\textit{Physics Reports}}, 
volume = {104},
pages = {237-258},
}

@article{Dirac2,
author = {Dirac, Paul A. M},
year = {1927},
title = {The quantum theory of the emission and absorption of radiation},
journal = {\textit{Proceedings of the Royal Society of London, Sries A}}, 
volume = {114},
pages = {243-265},
}

@article{Heisenberg,
author = {Heisenberg, Werner and Pauli Wolfgang},
year = {1929},
title = {Zur Quantendynamik der Wellenfelder}, 
journal = {\textit{Zeitschrift f\"{u}r Phisik}},
volume = {56},
pages = {1-16}, 
}

@book{Ohnuki,
author = {Ohnuki, Yoshio},
year = {1994},
title = {\textit{Ba no ryousiron (Quantum theory of fields)}},
note = {in Japanese},
publisher = {Iwanami Shoten},
address	= {Tokyo},
}

@incollection{Kohlenbach,
author = {Kohlenbach, Paul J},
year = {2005},
title = {Higher order reverse mathematics}, 
booktitle = {\textit{Reverse Mathematics 2001}}, 
editor = {Stephen. G  Simpson}, 
publisher = {Association for Symbolic Logic, A. K Peters}, 
address	= {Massachusetts},
pages = {281-295},        
}

@article{Drake,
author = {Drake, Frank R.},
title = {How recent work in mathematical logic relates to the foundations of mathematics},
journal = {\textit{Mathematical Intelligencer}}, 
volume = {7/4},
year = {1985},
pages = {27-35},
}

@book{Kanamori,
author = {Kanamori, Akihiro},
year = {1994},
title = {\textit{The Higher Infinite}},
publisher = {Springer},
address	= {New York},
}

@book{Nishimura,
author = {Nishimura, Toshio and Namba, Kanji},
year = {1985},
title= {\textit{Kouriteki Shuugouron (Axiomatic Set Theory)}},
note = {in Japanese},
publisher = {Kyouritu Shuppan},
address	= {Tokyo},
}

@incollection{Wheeler,
author = {Wheeler, John A},
year = {1985},
title = {Physics in Copenhagen in 1934 and 1935},
booktitle = {\textit{Niels Bohr, A Centenary Volume}},
editor = { A. P.  French and P.  G. Kennedy},
publisher = {Harvard University Press},
address	= {Cambridge; Massachusetts},
pages= {221-226},
}

@article{Cantor3,
author = {Cantor, Georg},
year = {1885},
title = {\"{U}ber verschiedene Theoreme aus der Theorie der Punktmengen in einem n-fach ausgedehnten stetigen Raume Gn. Zweite Mitteilung},
journal = {\textit{Acta Mathematica}},
volume = {7},
pages  = {105-124},
note = {Georg Cantor, Abhandlungen Mathematischen und Philosophischen Inhalts, ed. Ernst Zermelo, 1932, Reprinted by Georg Olms, Hildesheim, 1966},
}

@book{Simpson2,
author = {Simpson, Stephen G},
year = {2009},
title = {\textit{Subsystems of Second Order Arithmetic}},
edition = {second}, 
publisher = {Cambridge University Press},
address	= {New York},
}