REFERENCES

Aristotle (1984). The Complete Works of Aristotle, ed. J. Barnes. Princeton, NJ: Princeton University Press.

Boole, G. (1847). The Mathematical Analysis of Logic : Being an Essay Towards a Calculus of Deductive Reasoning. Cambridge, UK: Macmillan, Barclay, & Macmillan.

Boole, G. (1854). An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities. London: Walton and Maberly.

Boyer, C. B. and U. C. Merzbach (1991). A History of Mathematics (2nd ed.). New York: John Wiley & Sons, Inc.

Burali-Forti, C. (1897). Una questione sui numeri transfiniti. Rendiconti del Circolo Matematico di Palermo 11(1), 154–164.

Cantor, G. (1874). Ueber eine Eigenschaft des Inbegriffs aller reellen algebraischen Zahlen. Journal Fur Die Reine Und Angewandte Mathematik 77, 258–262.

Cantor, G. (1888). Mitteilungen zur Lehre vom Transfiniten. Zeitschrift für Philosophie und philosophische Kritik 91, 81–125.

Cantor, G. (1891). Über eine elementare Frage def Mannigfaltigkeitslehre. Jahresbericht der Deutschen Mathematiker-Vereinigung 1, 75–78.

Cantor, G. (1932). Gesammelte Abhandlungen mathematischen und philosophischen Inhalts. Berlin: Springer-Verlag.

Chang, C. C. and H. J. Keisler (1990). Model Theory (3rd ed.). Studies in Logic and the Foundations of Mathematics. Amsterdam: North Holland.

Church, A. (1956). Introduction to Mathematical Logic. Princeton, NJ: Princeton University Press.

Ciesielski, K. (1997). Set Theory for the Working Mathematician. London Mathematical Society Student Texts. Cambridge, UK: Cambridge University Press.

Cohen, P. J. (1963). The independence of the continuum hypothesis. Proceedings of the National Academy of Sciences of the United States of America 50(6), 1143–1148.

Copi, I. M. (1979). Symbolic Logic (5th ed.). New York: Macmillan Publishing.

Dauben, J. W. (1979). George Cantor: His Mathematics and Philosophy of the Infinite. Princeton, NJ: Princeton University Press.

De Morgan, A. (1847). Formal Logic: or, the Calculus of Inference, Necessary and Probable. London: Taylor and Walton.

Dedekind, R. (1893). Was sind und was sollen die Zahlen? Braunschweig: F. Vieweg.

Dedekind, R. (1901). Essays on the Theory of Numbers, trans. W. W. Beman. Chicago: Open Court.

Descartes, R. (1985). The Philosophical Writings of Descartes, eds. J. Cottingham, R. Stoothoff, and D. Murdoch. Cambridge, UK: Cambridge University Press.

Doets, K. (1996). Basic Model Theory. Stanford: CSLI Publications.

Drake, F. R. (1974). Set Theory: An Introduction to Large Cardinals, Volume 76 of Studies in Logic and Foundations of Mathematics. Amsterdam: North-Holland.

Ebbinghaus, H., J. Flum, and W. Thomas (1984). Mathematical Logic. Undergraduate Texts in Mathematics. New York: Springer-Verlag.

Ebbinghaus, H. and V. Peckhaus (2007). Ernst Zermelo: An Approach to His Life and Work. Berlin: Springer.

Eklof, P. C. (1976). Whitehead's problem is undecidable. American Mathematical Monthly 83, 775–788.

Eklof, P. C. and A. H. Mekler (2002). Almost Free Modules: Set-theoretic Methods (revised ed.). Amsterdam: North-Holland.

Enderton, H. B. (1977). Elements of Set Theory. San Diego: Academic Press.

Euclid (1925). The Elements, ed. T. Heath. Reprint, New York: Dover, 1956.

Ewald, W. B. (2007). From Kant to Hilbert: A Source Book in the Foundations of Mathematics. Oxford: Oxford University Press.

Fibonacci and L. E. Sigler (2002). Fibonacci's Liber Abaci: A Translation into Modern English of Leonardo Pisano's Book of Calculuation. Sources and Studies in the History of Mathematics and Physical Sciences. New York: Springer.

Fraenkel, A. A. (1922). Zu den Grundlagen der Cantor-Zermeloschen Mengenlehre. Mathematische Annalen 86, 230–237.

Fraleigh, J. B. (1999). A First Course in Abstract Algebra (6th ed.). Reading, MA: Addison-Wesley.

Frege, G. (1879). Begriffsschrift, Eine Der Arithmetischen Nachgebildete Formelsprache Des Reinen Denkens. Halle a/S.

Frege, G. (1884). Die Grundlagen Der Arithmetik: Eine Logisch Mathematische Untersuchung Über Den Begriff Der Zahl. Breslau: W. Koebner.

Frege, G. (1893). Grundgesetze Der Arithmetik : Begriffsschriftlich Abgeleitet. Jena: H. Pohle.

Gödel, K. (1929). Über die Vollständigkeit des Logikkalküls. Ph. D. thesis, University of Vienna.

Gödel, K. (1930). Die Vollständigkeit der Axiome des logischen Functionenkalküls. Monatshefte für Mathematik und Physik 37, 349–360.

Gödel, K. (1931). Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, I. Monatshefte für Mathematik und Physik 38, 173–198.

Gödel, K. (1940). Consistency of the Continuum Hypothesis. Princeton, NJ: Princeton University Press.

Halmos, P. R. (1960). Naive Set Theory. New York: Springer-Verlag.

Henkin, L. (1949). The Completeness of Formal Systems. Ph. D. thesis, Princeton University, Princeton, NJ.

Herrlich, H. (2006). Axiom of Choice. Lecture Notes in Mathematics. Berlin: Springer.

Hilbert, D. (1899). Grundlagen der Geometrie. Leipzig: Teubner.

Hilbert, D. (1902). Mathematical problems, trans. M. F. W. Newson. Bulletin of the American Mathematical Society 8, 437–479.

Hodges, W. (1993). Model Theory. Encyclopedia of Mathematics and its Applications. Cambridge, U.K.: Cambridge University Press.

Hofstadter, D. R. (1989). Gödel, Escher, Bach: an Eternal Golden Braid. Reprint, New York: Vintage Books.

Jech, T. (1973). The Axiom of Choice, Volume 75 of Studies in Logic and the Foundations of Mathematics. Amsterdam: North-Holland.

Jech, T. (2003). Set Theory: The Third Millennium Edition. Springer Monographs in Mathematics. Berlin: Springer.

Jensen, R. B. (1972). The fine structure of the constructible hierarchy. Annals of Mathematical Logic 4(3), 229–308.

Kaye, R. (1991). Models of Peano Arithmetic, eds. D. S. Angus Macintyre, John Shepherdson. Oxford, UK: Clarendon Press.

Kline, M. (1972). Mathematical Thought from Ancient to Modern Times. New York: Oxford University Press.

Kneale, W. and M. Kneale (1964). The Development of Logic. Oxford, UK: Clarendon Press.

König, J. (1905). Zum Kontinuum-problem. Mathematische Annalen 60(2), 177–180.

König, J. (1906). Sur la théorie des ensembles. Comptes rendus hebdomadaires des séances de l'Académie des sciences 143, 110–112.

Kunen, K. (1990). Set Theory: An Introduction to Independence Proofs, Volume 102 of Studies in Logic and the Foundations of Mathematics. Amsterdam: North-Holland.

Kuratowski, K. (1921). Sur la notion de l'order dans la théorie des ensembles. Fundamenta Mathematicae 2, 161–171.

Kuratowski, K. (1922). Sur l'opération a de l'analysis situs. Fundamenta Mathematicae 3, 182–199.

Leary, C. C. (2000). A Friendly Introduction to Mathematical Logic. Upper Saddle River, NJ: Prentice Hall.

Leibniz, G. W. (1666). Dissertatio de arte combinatoria, in qua ex arithmeticae fundamentis complicationum ac transpositionum doctrina novis praeceptis extruitur, & usus ambarum per universum scientiarum orbem ostenditur; nova etiam artis meditandi, seu logicae inventionis semina sparguntur. Lipsiae, apud Joh. Simon Fickium et Joh. Polycarp. Seuboldum, Literis Spörelianis.

Levy, A. (1979). Basic Set Theory. Perspectives in Mathematical Logic. Berlin: Springer-Verlag.

Löwenheim, L. (1915). Über Möglichkeiten im Relativkalkül. Mathematische Annalen 76(4), 447–470.

Łukasiewicz, J. (1930). Elementy logiki matematycznej. Warsaw: s.n.

Łukasiewicz, J. (1951). Aristotle's Syllogistic From the Standpoint of Modern Formal Logic. Oxford, UK: Clarendon Press.

Mal'tsev, A. I. (1936). Untersuchungen aus dem Gebiete der mathematischen Logik. Matematicheskii Sbornik 1(43), 323–336.

Martin, D. A. and R. M. Solovay (1970). Internal Cohen extensions. Annals of Mathematical Logic 2(2), 143–178.

Mirimanoff, D. (1917). Les antinomies de Russel et de Burali-Forti et le problème fondamental de la théorie des ensembles. L'Enseignement Mathématique 19, 37–52.

Pascal, B. (1665). Traité du triangle arithmetique, avec quelques autres petits traitez sur la mesme matrière. Paris: chez G. Desprez.

Peano, G. (1889). Arithmetices principia: nova methodo. Augustae Taurinorum [Torino]: Fratres Bocca.

Reid, C. (1996). Hilbert. New York: Copernicus.

Rosen, K. H. (1993). Elementary Number Theory and Its Applications (3rd ed.). Reading, MA: Addison-Wesley.

Rubin, H. and J. E. Rubin (1985). Equivalents of the Axiom of Choice, II, Volume 116 of Studies in Logic and the Foundations of Mathematics. Amsterdam: North-Holland.

Rubin, J. E. (1973). The compactness theorem in mathematical logic. Mathematics Magazine 46(5), 261–265.

Shelah, S. (1974). Infinite abelian groups, Whitehead problem and some constructions. Isreal Journal of Mathematics 18(3), 243–256.

Skolem, T. (1922). Einige Bemerkungen zur axiomatischen Begründung der Mengenlehre. In Proceedings of the 5th Scandinavian Mathematicians' Congress in Helsinki, pp. 217–32.

Suppes, P. (1972). Axiomatic Set Theory. New York: Dover Publications.

Tarski, A. (1935). Der wahrheitsbegriff in den formalisierten sprachen. Studia Philosophica 1, 261–405.

Tarski, A. (1983). Logic, Semantics, Metamathematics: Papers from 1923 to 1938, trans. J. H. Woodger. Indianapolis: Hackett Publishing Company.

Tarski, A. and R. L. Vaught (1957). Arithmetical extensions of relational systems. Compositio Mathematica 13, 81–102.

van Dalen, D. (1994). Logic and Structure (3rd ed.). Berlin: Springer-Verlag.

van Dalen, D., H. C. Doets, and H. de Swart (1978). Sets: Naive, Axiomatic and Applied, Volume 106 of International Series in Pure and Applied Mathematics. Oxford, UK: Pergamon Press.

Van Heijenoort, J. (1971). Frege and Gödel: Two Fundamental Texts in Mathematical Logic. Cambridge MA: Harvard University Press.

Van Heijenoort, J. (1977). From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931. Source Books in History of Sciences. Cambridge, MA: Harvard University Press.

Venn, J. (1894). Symbolic Logic (2nd ed.). London: Macmillan.

von Neumann, J. (1923). Zur Einführung der transfiniten Zahlen. Acta literarum ac scientiarum Regiae Universitatis Hungaricae Francisco-Josephinae, Sectio scientiarum mathematicarum 1, 199–208.

von Neumann, J. (1928). Über die Definition durch transfinite Induktion und verwandte Fragen der allgemeinen Mengenlehre. Mathematische Annalen 99, 373–391.

von Neumann, J. (1929). Über eine Widerspruchsfreiheitsfrage der axiomatischen Mengenlehre. Journal für die reine und angewandte Mathematik 160, 227–241.

Whitehead, A. N. and B. Russell (1910). Principia Mathematica (2nd ed.). Cambridge, UK: Cambridge University Press.

Whitehead, J. H. C. (1950). Simple homotopy types. American Journal of Mathematics 72(1), 1–57.

Wussing, H. (1984). The Genesis of the Abstract Group Concept, ed. H. Grant, trans. A. Shenitzer. Cambridge, MA: MIT Press.

Zermelo, E. (1908). Untersuchungen über die grundlagen der mengenlehre. Mathematische Annalen 65, 261–281.

Zermelo, E. (1930). Über Grenzzahlen und Mengenbereiche. Neue Untersuchungen über die Grundlagen der Mengenlehre. Fundamenta mathematicae 16, 29–47.

Zorn, M. (1935). A remark on method in transfinite algebra. Bulletin of the American Mathematical Society 41, 667–670.

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