Các tác phẩm của Gödel

• Kurt Gödel, 1931, "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, I", Monatshefte für Mathematik und Physik, v. 38 n. 1, pp. 173–198.
• —, 1931, "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, I", in Solomon Feferman, ed., 1986. Kurt Gödel Collected works, Vol. I. Oxford University Press, pp. 144–195. ISBN 978-0195147209. The original German with a facing English translation, preceded by an introductory note by Stephen Cole Kleene.
• —, 1951, "Some basic theorems on the foundations of mathematics and their implications", in Solomon Feferman, ed., 1995. Kurt Gödel Collected works, Vol. III, Oxford University Press, pp. 304–323. ISBN 978-0195147223.

Bản dịch các tác phẩm của Gödel khi ông còn sống

• B. Meltzer (translation) and R. B. Braithwaite (Introduction), 1962. On Formally Undecidable Propositions of Principia Mathematica and Related Systems, Dover Publications, New York (Dover edition 1992), ISBN 0-486-66980-7 (pbk.) This contains a useful translation of Gödel's German abbreviations on pp. 33–34. As noted above, typography, translation and commentary is suspect. Unfortunately, this translation was reprinted with all its suspect content by

• Stephen Hawking editor, 2005. God Created the Integers: The Mathematical Breakthroughs That Changed History, Running Press, Philadelphia, ISBN 0-7624-1922-9. Gödel's paper appears starting on p. 1097, with Hawking's commentary starting on p. 1089.

• Martin Davis editor, 1965. The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable problems and Computable Functions, Raven Press, New York, no ISBN. Gödel's paper begins on page 5, preceded by one page of commentary.
• Jean van Heijenoort editor, 1967, 3rd edition 1967. From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931, Harvard University Press, Cambridge Mass., ISBN 0-674-32449-8 (pbk). van Heijenoort did the translation. He states that "Professor Gödel approved the translation, which in many places was accommodated to his wishes." (p. 595). Gödel's paper begins on p. 595; van Heijenoort's commentary begins on p. 592.
• Martin Davis editor, 1965, ibid. "On Undecidable Propositions of Formal Mathematical Systems." A copy with Gödel's corrections of errata and Gödel's added notes begins on page 41, preceded by two pages of Davis's commentary. Until Davis included this in his volume this lecture existed only as mimeographed notes.

Tác phẩm của các tác giả khác

• George Boolos, 1989, "A New Proof of the Gödel Incompleteness Theorem", Notices of the American Mathematical Society, v, 36, pp. 388–390 and p. 676, reprinted in Boolos, 1998, Logic, Logic, and Logic, Harvard Univ. Press. ISBN 0-674-53766-1
• Bernd Buldt, 2014, "The Scope of Gödel's First Incompleteness Theorem", Logica Universalis, v. 8, pp. 499–552. doi:10.1007/s11787-014-0107-3
• Arthur Charlesworth, 1980, "A Proof of Godel's Theorem in Terms of Computer Programs", Mathematics Magazine, v. 54 n. 3, pp. 109–121. JSTOR 2689794
• Martin Davis, 2006, "The Incompleteness Theorem", Notices of the AMS, v. 53 n. 4, pp. 414.
• Jean van Heijenoort, 1963, "Gödel's Theorem" in Edwards, Paul, ed., Encyclopedia of Philosophy, v. 3. Macmillan, pp. 348–57.
• Geoffrey Hellman, 1981, "How to Gödel a Frege-Russell: Gödel's Incompleteness Theorems and Logicism", Noûs, v. 15 n. 4, Special Issue on Philosophy of Mathematics, pp. 451–468.
• David Hilbert, 1900, "Mathematical Problems." English translation of a lecture delivered before the International Congress of Mathematicians at Paris, containing Hilbert's statement of his Second Problem.
• Martin Hirzel, 2000, On formally undecidable propositions of Principia Mathematica and related systems I.. An English translation of Gödel's paper.
• Makoto Kikuchi and Kazayuki Tanaka, 1994, "On formalization of model-theoretic proofs of Gödel's theorems", Notre Dame Journal of Formal Logic, v. 5 n. 3, pp. 403–412. doi:10.1305/ndjfl/1040511346 Bản mẫu:Mr
• Stephen Cole Kleene, 1943, "Recursive predicates and quantifiers", reprinted from Transactions of the American Mathematical Society, v. 53 n. 1, pp. 41–73 in Martin Davis 1965, The Undecidable (loc. cit.) pp. 255–287.
• Panu Raatikainen, 2015, "Gödel's Incompleteness Theorems", Stanford Encyclopedia of Philosophy. Truy cập ngày 3 tháng 4 năm 2015.
• Panu Raatikainen, 2005, "On the philosophical relevance of Gödel's incompleteness theorems", Revue Internationale de Philosophie 59 (4):513-534.
• John Barkley Rosser, 1936, "Extensions of some theorems of Gödel and Church", reprinted from the Journal of Symbolic Logic, v. 1 (1936) pp. 87–91, in Martin Davis 1965, The Undecidable (loc. cit.) pp. 230–235.
• —, 1939, "An Informal Exposition of proofs of Gödel's Theorem and Church's Theorem", Reprinted from the Journal of Symbolic Logic, v. 4 (1939) pp. 53–60, in Martin Davis 1965, The Undecidable (loc. cit.) pp. 223–230
• C. Smoryński, 1982, "The incompleteness theorems", in Jon Barwise, ed., Handbook of Mathematical Logic, North-Holland, pp. 821–866. ISBN 978-0-444-86388-1
• Dan E. Willard, 2001, "Self-Verifying Axiom Systems, the Incompleteness Theorem and Related Reflection Principles", Journal of Symbolic Logic, v. 66 n. 2, pp. 536–596. doi:10.2307/2695030
• Richard Zach, 2003. "The Practice of Finitism: Epsilon Calculus and Consistency Proofs in Hilbert's Program" Synthese, v. 137 n. 1, pp. 211–259. doi:10.1023/A:1026247421383
• —, 2005, "Kurt Gödel, Paper on the incompleteness theorems" in Ivor Grattan-Guinness, ed. Landmark Writings in Western Mathematics, Elsevier, pp. 917–925. doi:10.1016/B978-044450871-3/50152-2

Những cuốn sách về các định lý

• Francesco Berto. There's Something about Gödel: The Complete Guide to the Incompleteness Theorem John Wiley and Sons. 2010.
• Norbert Domeisen, 1990. Logik der Antinomien. Bern: Peter Lang. 142 S. 1990. ISBN 3-261-04214-1. Bản mẫu:Zbl.
• Torkel Franzén, 2005. Gödel's Theorem: An Incomplete Guide to its Use and Abuse. A.K. Peters. ISBN 1-56881-238-8 MR2146326
• Douglas Hofstadter, 1979. Gödel, Escher, Bach: An Eternal Golden Braid. Vintage Books. ISBN 0-465-02685-0. 1999 reprint: ISBN 0-465-02656-7. MR530196
•  —, 2007. I Am a Strange Loop. Basic Books. ISBN 978-0-465-03078-1. ISBN 0-465-03078-5. MR2360307
• Stanley Jaki, OSB, 2005. The drama of the quantities. Real View Books.
• Per Lindström, 1997. Aspects of Incompleteness, Lecture Notes in Logic v. 10.
• J.R. Lucas, FBA, 1970. The Freedom of the Will. Clarendon Press, Oxford, 1970.
• Ernest Nagel, James Roy Newman, Douglas Hofstadter, 2002 (1958). Gödel's Proof, revised ed. ISBN 0-8147-5816-9. MR1871678
• Rudy Rucker, 1995 (1982). Infinity and the Mind: The Science and Philosophy of the Infinite. Princeton Univ. Press. MR658492
• Peter Smith, 2007. An Introduction to Gödel's Theorems. Cambridge University Press. MR2384958
• N. Shankar, 1994. Metamathematics, Machines and Gödel's Proof, Volume 38 of Cambridge tracts in theoretical computer science. ISBN 0-521-58533-3
• Raymond Smullyan, 1987. Forever Undecided ISBN 0192801414 - puzzles based on undecidability in formal systems
• —, 1991. Godel's Incompleteness Theorems. Oxford Univ. Press.
• —, 1994. Diagonalization and Self-Reference. Oxford Univ. Press. MR1318913
• —, 2013. The Godelian Puzzle Book: Puzzles, Paradoxes and Proofs. Courier Corporation. ISBN 978-0-486-49705-1.
• Hao Wang, 1997. A Logical Journey: From Gödel to Philosophy. MIT Press. ISBN 0-262-23189-1 MR1433803

Tác phẩm gồm nhiều tác giả

• Francesco Berto, 2009, "The Gödel Paradox and Wittgenstein's Reasons" Philosophia Mathematica (III) 17.
• John W. Dawson, Jr., 1997. Logical Dilemmas: The Life and Work of Kurt Gödel, A. K. Peters, Wellesley Mass, ISBN 1-56881-256-6.
• Rebecca Goldstein, 2005, Incompleteness: the Proof and Paradox of Kurt Gödel, W. W. Norton & Company. ISBN 0-393-05169-2
• Juliet Floyd và Hilary Putnam, 2000, "A Note on Wittgenstein's 'Notorious Paragraph' About the Gödel Theorem", Journal of Philosophy v. 97 n. 11, pp. 624–632.
• John Harrison, 2009, "Handbook of Practical Logic and Automated Reasoning", Cambridge University Press, ISBN 0521899575
• David Hilbert và Paul Bernays, Grundlagen der Mathematik, Springer-Verlag.
• John Hopcroft và Jeffrey Ullman 1979, Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, ISBN 0-201-02988-X
• James P. Jones, Undecidable Diophantine Equations, Bulletin of the American Mathematical Society, v. 3 n. 2, 1980, pp. 859–862.
• Stephen Cole Kleene, 1967, Mathematical Logic. Reprinted by Dover, 2002. ISBN 0-486-42533-9
• Russell O'Connor, 2005, "Essential Incompleteness of Arithmetic Verified by Coq", Lecture Notes in Computer Science v. 3603, pp. 245–260.
• Lawrence Paulson, 2013, "A machine-assisted proof of Gödel's incompleteness theorems for the theory of hereditarily finite sets", Review of Symbolic Logic, v. 7 n. 3, 484–498.
• Graham Priest, 1984, "Logic of Paradox Revisited", Journal of Philosophical Logic, v. 13,` n. 2, pp. 153–179.
• —, 2004, Wittgenstein's Remarks on Gödel's Theorem in Max Kölbel, ed., Wittgenstein's lasting significance, Psychology Press, pp. 207–227.
• —, 2006, In Contradiction: A Study of the Transconsistent, Oxford University Press, ISBN 0-19-926329-9
• Hilary Putnam, 1960, Minds and Machines in Sidney Hook, ed., Dimensions of Mind: A Symposium. New York University Press. Reprinted in Anderson, A. R., ed., 1964. Minds and Machines. Prentice-Hall: 77.
• Wolfgang Rautenberg, 2010, A Concise Introduction to Mathematical Logic, 3rd. ed., Springer, ISBN 978-1-4419-1220-6
• Victor Rodych, 2003, "Misunderstanding Gödel: New Arguments about Wittgenstein and New Remarks by Wittgenstein", Dialectica v. 57 n. 3, pp. 279–313. doi:10.1111/j.1746-8361.2003.tb00272.x
• Stewart Shapiro, 2002, "Incompleteness and Inconsistency", Mind, v. 111, pp 817–32. doi:10.1093/mind/111.444.817
• Alan Sokal và Jean Bricmont, 1999, Fashionable Nonsense: Postmodern Intellectuals' Abuse of Science, Picador. ISBN 0-312-20407-8
• Joseph R. Shoenfield (1967), Mathematical Logic. Reprinted by A.K. Peters for the Association for Symbolic Logic, 2001. ISBN 978-1-56881-135-2
• Jeremy Stangroom và Ophelia Benson, Why Truth Matters, Continuum. ISBN 0-8264-9528-1
• George Tourlakis, Lectures in Logic and Set Theory, Volume 1, Mathematical Logic, Cambridge University Press, 2003. ISBN 978-0-521-75373-9
• Avi Wigderson, 2010, "The Gödel Phenomena in Mathematics: A Modern View", in Kurt Gödel and the Foundations of Mathematics: Horizons of Truth, Cambridge University Press.
• Hao Wang, 1996, A Logical Journey: From Gödel to Philosophy, The MIT Press, Cambridge MA, ISBN 0-262-23189-1.
• Richard Zach, 2006, "Hilbert's program then and now", in Philosophy of Logic, Dale Jacquette (ed.), Handbook of the Philosophy of Science, v. 5., Elsevier, pp. 411–447.