Linked bibliography for the SEP article "Recursive Functions" by Walter Dean

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  • Ackermann, Wilhelm, 1928, “Über die Erfüllbarkeit gewisser Zählausdrücke”, Mathematische Annalen, 100: 638–649. doi:10.1007/BF01448869
  • Adams, Rod, 2011, An Early History of Recursive Functions and Computability: From Gödel to Turing, Boston: Docent Press.
  • Addison, J.W., 1954, On Some Points of the Theory of Recursive Functions, PhD thesis, University of Wisconsin.
  • –––, 1958, “Separation Principles in the Hierarchies of Classical and Effective Descriptive Set Theory”, Fundamenta Mathematicae, 46(2): 123–135. doi:10.4064/fm-46-2-123-135
  • –––, 1959, “Some Consequences of the Axiom of Constructibility”, Fundamenta Mathematicae, 46(3): 337–357. doi:10.4064/fm-46-3-337-357
  • Basu, Sankha S. and Stephen G. Simpson, 2016, “Mass Problems and Intuitionistic Higher-Order Logic”, Computability, 5(1): 29–47. doi:10.3233/COM-150041
  • Bimbó, Katalin, 2012, Combinatory Logic: Pure, Applied and Typed, Boca Raton, FL: Chapman & Hall.
  • Boolos, George S., John P. Burgess, and Richard C. Jeffrey, 2007, Computability and Logic, fifth edition, Cambridge: Cambridge University Press. doi:10.1017/CBO9780511804076
  • Calude, Cristian, Solomon Marcus, and Ionel Tevy, 1979, “The First Example of a Recursive Function Which Is Not Primitive Recursive”, Historia Mathematica, 6(4): 380–384. doi:10.1016/0315-0860(79)90024-7
  • Church, Alonzo, 1936a, “A Note on the Entscheidungsproblem”, Journal of Symbolic Logic, 1(1): 40–41. doi:10.2307/2269326
  • –––, 1936b, “An Unsolvable Problem of Elementary Number Theory”, American Journal of Mathematics, 58(2): 345–363. doi:10.2307/2371045
  • Clote, Peter and Evangelos Kranakis, 2002, Boolean Functions and Computation Models, (Texts in Theoretical Computer Science. An EATCS Series), Berlin, Heidelberg: Springer Berlin Heidelberg. doi:10.1007/978-3-662-04943-3
  • Cooper, S. Barry, 2004, Computability Theory, Boca Raton, FL: Chapman & Hall.
  • Cutland, Nigel, 1980, Computability: An Introduction to Recursive Function Theory, Cambridge: Cambridge University Press. doi:10.1017/CBO9781139171496
  • Davis, Martin (ed.), 1965, The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions, New York: Raven Press.
  • –––, 1982, “Why Gödel Didn’t Have Church’s Thesis”, Information and Control, 54(1–2): 3–24. doi:10.1016/S0019-9958(82)91226-8
  • Davis, Martin, Ron Sigal, and Elaine J. Weyuker, 1994, Computability, Complexity, and Languages: Fundamentals of Theoretical Computer Science, second edition, (Computer Science and Scientific Computing), Boston: Academic Press, Harcourt, Brace.
  • Dean, W., forthcoming, “Incompleteness via Paradox and Completeness”, The Review of Symbolic Logic, first online: 23 May 2019. doi:10.1017/S1755020319000212
  • Dedekind, Richard, 1888, Was Sind Und Was Sollen Die Zahlen?, Braunschweig: Vieweg.
  • Enderton, Herbert B., 2010, Computability Theory: An Introduction to Recursion Theory, Burlington, MA: Academic Press.
  • Epstein, Richard and Walter A. Carnielli, 2008, Computability: Computable Functions, Logic, and the Foundations of Mathematics, Socorro, NM: Advance Reasoing Forum.
  • Ewald, William Bragg (ed.), 1996, From Kant to Hilbert: A Source Book in the Foundations of Mathematics., New York: Oxford University Press.
  • Feferman, Solomon, 1995, “Turing in the land of \(O(z)\)”, in The Universal Turing Machine a Half-Century Survey, Rolf Herken (ed.), Berlin: Springer, pp. 103–134.
  • Fibonacci, 1202 [2003], Fibonacci’s Liber Abaci: A Translation into Modern English of Leonardo Pisano’s Book of Calculation, L. E. Sigler (ed.), Berlin: Springer.
  • Friedberg, R. M., 1957, “Two Recursively Enumerable Sets of Incomparable Degrees of Unsolvability (Solution of Post’s Problem, 1944)”, Proceedings of the National Academy of Sciences, 43(2): 236–238. doi:10.1073/pnas.43.2.236
  • Gandy, Robin, 1980, “Church’s Thesis and Principles for Mechanisms”, in The Kleene Symposium, Jon Barwise, H. Jerome Keisler, and Kenneth Kunen (eds.), (Studies in Logic and the Foundations of Mathematics 101), Amsterdam: Elsevier, 123–148. doi:10.1016/S0049-237X(08)71257-6
  • Gödel, Kurt, 1931, “Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, I” (On Formally Undecidable Propositions of Principia Mathematica and Related Systems I), Monatshefte für Mathematik und Physik, 38: 173–198. Reprinted in Gödel 1986: 144–195.
  • –––, 1934, “On Undecidable Propositions of Formal Mathematical Systems”, Princeton lectures. Reprinted in Godel 1986: 338-371.
  • –––, 1986, Collected Works. I: Publications 1929–1936, Solomon Feferman, John W. Dawson, Jr, Stephen C. Kleene, Gregory H. Moore, Robert M. Solovay, and Jean van Heijenoort (eds.), Oxford: Oxford University Press.
  • –––, 2003, Collected Works. V: Correspondence H–Z, Solomon Feferman, John W. Dawson, Jr, Warren Goldfrab, Charles Parsons, and Wilfried Sieg (eds.), Oxford: Oxford University Press.
  • Grassmann, Hermann, 1861, Lehrbuch Der Arithmetik Für Höhere Lehranstalten, Berin: Th. Chr. Fr. Enslin.
  • Greibach, Sheila A., 1975, Theory of Program Structures: Schemes, Semantics, Verification, (Lecture Notes in Computer Science 36), Berlin/Heidelberg: Springer-Verlag. doi:10.1007/BFb0023017
  • Grzegorczyk, Andrzej, 1953, “Some Classes of Recursive Functions”, Rozprawy Matematyczne, 4: 3–45.
  • Grzegorczyk, A., A. Mostowski, and C. Ryll-Nardzewski, 1958, “The Classical and the ω-Complete Arithmetic”, The Journal of Symbolic Logic, 23(2): 188–206. doi:10.2307/2964398
  • Heijenoort, Jean van (ed.), 1967, From Frege to Gödel : A Source Book in Mathematical Logic, 1879–1931, Cambridge, MA: Harvard University Press.
  • Herbrand, Jacques, 1930, “Les Bases de la Logique Hilbertienne”, Revue de Metaphysique et de Morale, 37(2): 243–255.
  • –––, 1932, “Sur La Non-Contradiction de l’Arithmétique.”, Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal), 166: 1–8. doi:10.1515/crll.1932.166.1
  • Hilbert, David, 1900, “Mathematische Probleme. Vortrag, Gehalten Auf Dem Internationalen Mathematiker-Congress Zu Paris 1900”, Nachrichten von Der Gesellschaft Der Wissenschaften Zu Göttingen, Mathematisch-Physikalische Klasse, 253–297. English translation as “Mathematical Problems” in Ewald, 1996, 1096–1105.
  • –––, 1905, “Über Die Grundlagen Der Logik Und Der Arithmetik”, in Verhandlungen Des 3. Internationalen Mathematiker-Kongresses : In Heidelberg Vom 8. Bis 13. August 1904, Leipzig: Teubner, pp. 174–185. English translation as “On the foundations of logic and and arithmetic” in van Heijenoort, 1967.
  • –––, 1920, “Lectures on Logic ‘Logic-Kalkül’ (1920)”, reprinted in Hilbert 2013: 298–377.
  • –––, 1922, “Neubegründung der Mathematik. Erste Mitteilung”, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 1(1): 157–177. English translation as “The new grounding of mathematics: First report” in Ewald 1996, 1115–1134. doi:10.1007/BF02940589
  • –––, 1923, “Die logischen Grundlagen der Mathematik”, Mathematische Annalen, 88(1–2): 151–165. English translation as “The logical foundations of mathematics” in Ewald 1996, 1134–1148. doi:10.1007/BF01448445
  • –––, 1926, “Über das Unendliche”, Mathematische Annalen, 95: 161–190. English translation as “On the infinite” in van Heijenoort 1967, 367–292. doi:10.1007/BF01206605
  • –––, 1930, “Probleme der Grundlegung der Mathematik”, Mathematische Annalen, 102: 1–9. English translation as “Problems of the Grounding of Mathematics” in Mancosu 1998, 223–233. doi:10.1007/BF01782335
  • Hilbert, David, 2013, David Hilbert’s Lectures on the Foundations of Arithmetic and Logic 1917–1933, William Ewald and Wilfried Sieg (eds.), Berlin, Heidelberg: Springer Berlin Heidelberg. doi:10.1007/978-3-540-69444-1
  • Hilbert, David and Wilhelm Ackermann, 1928, Grundzüge der theoretischen Logik, first edition, Berlin: J. Springer.
  • Hilbert, David and Paul Bernays, 1934, Grundlagen der Mathematik, Vol. I, Berlin: Springer.
  • –––, 1939, Grundlagen der Mathematik, Vol. II, Berlin: Springer.
  • Hinman, Peter G., 1978, Recursion-Theoretic Hierarchies, Berlin: Springer.
  • Hopcroft, John and Jeffrey Ulman, 1979, Introduction to Automata Theory, Languages, and Computation, Reading, MA: Addison-Wesley.
  • Kaye, Richard, 1991, Models of Peano Arithmetic, (Oxford Logic Guides, 15), Oxford: Clarendon Press.
  • Kechris, Alexander S., 1995, Classical Descriptive Set Theory, Berlin: Springer. doi:10.1007/978-1-4612-4190-4
  • Kleene, S. C., 1936a, “General Recursive Functions of Natural Numbers”, Mathematische Annalen, 112(1): 727–742. doi:10.1007/BF01565439
  • –––, 1936b, “λ-Definability and Recursiveness”, Duke Mathematical Journal, 2(2): 340–353. doi:10.1215/S0012-7094-36-00227-2
  • –––, 1938, “On Notation for Ordinal Numbers”, Journal of Symbolic Logic, 3(4): 150–155. doi:10.2307/2267778
  • –––, 1943, “Recursive Predicates and Quantifiers”, Transactions of the American Mathematical Society, 53(1): 41–41. doi:10.1090/S0002-9947-1943-0007371-8
  • –––, 1952, Introduction to Metamathematics, Amsterdam: North-Holland.
  • –––, 1955a, “Arithmetical Predicates and Function Quantifiers”, Transactions of the American Mathematical Society, 79(2): 312–312. doi:10.1090/S0002-9947-1955-0070594-4
  • –––, 1955b, “Hierarchies of Number-Theoretic Predicates”, Bulletin of the American Mathematical Society, 61(3): 193–214. doi:10.1090/S0002-9904-1955-09896-3
  • –––, 1955c, “On the Forms of the Predicates in the Theory of Constructive Ordinals (Second Paper)”, American Journal of Mathematics, 77(3): 405–428. doi:10.2307/2372632
  • Kleene, S. C. and Emil L. Post, 1954, “The Upper Semi-Lattice of Degrees of Recursive Unsolvability”, The Annals of Mathematics, 59(3): 379–407. doi:10.2307/1969708
  • Kolmogorov, Andrei, 1932, “Zur Deutung der intuitionistischen Logik”, Mathematische Zeitschrift, 35(1): 58–65. doi:10.1007/BF01186549
  • Kondô, Motokiti, 1939, “Sur l’uniformisation des Complémentaires Analytiques et les Ensembles Projectifs de la Seconde Classe”, Japanese Journal of Mathematics :Transactions and Abstracts, 15: 197–230. doi:10.4099/jjm1924.15.0_197
  • Kreisel, George, 1960, “La Prédicativité”, Bulletin de La Société Mathématique de France, 79: 371–391. doi:10.24033/bsmf.1554
  • Kreisel, George and Gerald E. Sacks, 1965, “Metarecursive Sets”, Journal of Symbolic Logic, 30(3): 318–338. doi:10.2307/2269621
  • Lachlan, A. H., 1966, “Lower Bounds for Pairs of Recursively Enumerable Degrees”, Proceedings of the London Mathematical Society, s3-16(1): 537–569. doi:10.1112/plms/s3-16.1.537
  • –––, 1968, “Distributive Initial Segments of the Degrees of Unsolvability”, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik/Mathematical Logic Quarterly, 14(30): 457–472. doi:10.1002/malq.19680143002
  • Lachlan, A.H and R.I Soare, 1980, “Not Every Finite Lattice Is Embeddable in the Recursively Enumerable Degrees”, Advances in Mathematics, 37(1): 74–82. doi:10.1016/0001-8708(80)90027-4
  • Lusin, Nicolas, 1927, “Sur Les Ensembles Analytiques”, Fundamenta Mathematicae, 10: 1–95. doi:10.4064/fm-10-1-1-95
  • Mancosu, Paolo, (ed.), 1998, From Brouwer to Hilbert: The Debate on the Foundations of Mathematics in the 1920s, Oxford: Oxford University Press.
  • McCarthy, John, 1961, “A Basis for a Mathematical Theory of Computation, Preliminary Report”, in Papers Presented at the May 9-11, 1961, Western Joint IRE-AIEE-ACM Computer Conference on - IRE-AIEE-ACM ’61 (Western), Los Angeles, California: ACM Press, 225–238. doi:10.1145/1460690.1460715
  • Médvédév, Ú. T., 1955, “Stépéni trudnosti massovyh problém” (Degrees of Difficulty of Mass Problems), Doklady Akadémii Nauk SSSR, 104: 501–504.
  • Moschovakis, Yiannis N., 1989, “The Formal Language of Recursion”, The Journal of Symbolic Logic, 54(4): 1216–1252. doi:10.2307/2274814
  • –––, 1994, Notes on Set Theory, (Undergraduate Texts in Mathematics), New York, NY: Springer New York. doi:10.1007/978-1-4757-4153-7
  • –––, 2009, Descriptive Set Theory, second edition, Providence, RI: American Mathematical Society.
  • –––, 2010, “Kleene’s Amazing Second Recursion Theorem”, The Bulletin of Symbolic Logic, 16(2): 189–239. doi:10.2178/bsl/1286889124
  • Mostowski, Andrzej, 1947, “On Definable Sets of Positive Integers”, Fundamenta Mathematicae, 34: 81–112. doi:10.4064/fm-34-1-81-112
  • Muchnik, A. A., 1956, “On the Unsolvability of the Problem of Reducibility in the Theory of Algorithms”, Doklady Akadémii Nauk SSSR, 108: 194–197.
  • Murawski, Roman, 1999, Recursive Functions and Metamathematics: Problems of Completeness and Decidability, Goedel’s Theorems, Dordrecht, Boston: Kluwer.
  • Myhill, John, 1955, “Creative sets”, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik/Mathematical Logic Quarterly, 1(2): 97–108. doi:10.1002/malq.19550010205
  • Odifreddi, Piergiogio, 1989, Classical Recursion Theory. volume 1: The Theory of Functions and Sets of Natural Numbers, (Studies in Logic and the Foundations of Mathematics 125), Amsterdam: North-Holland
  • –––, 1999a, Classical Recursion Theory. volume 2, (Studies in Logic and the Foundations of Mathematics 143), Amsterdam: North-Holland.
  • –––, 1999b, “Reducibilities”, in Handbook of Computability Theory, Edward R. Griffor (ed.), (Studies in Logic and the Foundations of Mathematics 140), Amsterdam: Elsevier, 89–119. doi:10.1016/S0049-237X(99)80019-6
  • Owings, James C., 1973, “Diagonalization and the Recursion Theorem.”, Notre Dame Journal of Formal Logic, 14(1): 95–99. doi:10.1305/ndjfl/1093890812
  • Peano, Giuseppe, 1889, Arithmetices Principia, Nova Methodo Exposita, Turin: Bocca.
  • Peirce, C. S., 1881, “On the Logic of Number”, American Journal of Mathematics, 4(1/4): 85–95. doi:10.2307/2369151
  • Péter, Rózsa, 1932, “Rekursive Funktionen”, in Verhandlungen Des Internationalen Mathematiker- Kongresses Zürich, Vol. 2, pp. 336–337.
  • –––, 1935, “Konstruktion nichtrekursiver Funktionen”, Mathematische Annalen, 111(1): 42–60. doi:10.1007/BF01472200
  • –––, 1959, “Rekursivität und Konstruktivität”, in Constructivity in Mathematics, Arend Heyting (ed.), North-Holland, Amsterdam, pp. 226–233.
  • –––, 1967, Recursive Functions, István Földes (trans.), New York: Academic Press.
  • Poincaré, Henri, 1906, “Les Mathématiques et La Logique”, Revue de Métaphysique et de Morale, 14(3): 294–317.
  • Post, Emil L., 1944, “Recursively Enumerable Sets of Positive Integers and Their Decision Problems”, Bulletin of the American Mathematical Society, 50(5): 284–317. doi:10.1090/S0002-9904-1944-08111-1
  • –––, 1965, “Absolutely unsolvable problems and relatively undecidable propositions: Account of an anticipation” (1941) in The undecidable M. Davis, ed., New York: Raven Press, 338–433.
  • Priest, Graham, 1997, “On a Paradox of Hilbert and Bernays”, Journal of Philosophical Logic, 26(1): 45–56. doi:10.1023/A:1017900703234
  • Putnam, Hilary, 1965, “Trial and Error Predicates and the Solution to a Problem of Mostowski”, Journal of Symbolic Logic, 30(1): 49–57. doi:10.2307/2270581
  • Rice, H. G., 1953, “Classes of Recursively Enumerable Sets and Their Decision Problems”, Transactions of the American Mathematical Society, 74(2): 358–358. doi:10.1090/s0002-9947-1953-0053041-6 (Scholar)
  • Robinson, Raphael, 1947, “Primitive Recursive Functions”, Bulletin of the American Mathematical Society, 53(10): 925–942. doi:10.1090/S0002-9904-1947-08911-4
  • Rogers, Hartley, 1987, Theory of Recursive Functions and Effective Computability, Cambridge, MA: MIT Press.
  • Rose, H. E., 1984, Subrecursion: Functions and Hierarchies, (Oxford Logic Guides, 9), Oxford: Clarendon Press.
  • Sacks, Gerald E., 1963a, Degrees of Unsolvability, Princeton, NJ: Princeton University Press.
  • –––, 1963b, “On the Degrees Less than 0′”, The Annals of Mathematics, 77(2): 211–231. doi:10.2307/1970214
  • –––, 1964, “The Recursively Enumerable Degrees Are Dense”, The Annals of Mathematics, 80(2): 300–312. doi:10.2307/1970393
  • –––, 1990, Higher Recursion Theory, Berlin: Springer.
  • Schwichtenberg, Helmut and Stanley S. Wainer, 2011, Proofs and Computations, Cambridge: Cambridge University Press. doi:10.1017/CBO9781139031905
  • Shepherdson, J. C. and H. E. Sturgis, 1963, “Computability of Recursive Functions”, Journal of the ACM, 10(2): 217–255. doi:10.1145/321160.321170
  • Shoenfield, Joseph R., 1959, “On Degrees of Unsolvability”, The Annals of Mathematics, 69(3): 644–653. doi:10.2307/1970028 (Scholar)
  • –––, 1960, “Degrees of Models”, Journal of Symbolic Logic, 25(3): 233–237. doi:10.2307/2964680
  • –––, 1967, Mathematical Logic, (Addison-Wesley serices in logic), Reading, MA: Addison-Wesley.
  • –––, 1971, Degrees of Unsolvability, Amsterdam: North-Holland.
  • Shore, Richard A. and Theodore A. Slaman, 1999, “Defining the Turing Jump”, Mathematical Research Letters, 6(6): 711–722. doi:10.4310/MRL.1999.v6.n6.a10
  • Sieg, Wilfried, 1994, “Mechanical Procedures and Mathematical Experiences”, in Mathematics and Mind, Alexander George (ed.), Oxford: Oxford University Press, pp. 71–117.
  • –––, 1997, “Step by Recursive Step: Church’s Analysis of Effective Calculability”, Bulletin of Symbolic Logic, 3(2): 154–180. doi:10.2307/421012
  • –––, 2005, “Only two letters: The correspondence between Herbrand and Gödel”, Bulletin of Symbolic Logic, 11(2): 172–184. doi:10.2178/bsl/1120231628
  • –––, 2009, “On Computability”, in Philosophy of Mathematics, Andrew D. Irvine (ed.), (Handbook of the Philosophy of Science), Amsterdam: Elsevier, 535–630. doi:10.1016/B978-0-444-51555-1.50017-1
  • Simpson, Stephen G., 1977, “First-Order Theory of the Degrees of Recursive Unsolvability”, The Annals of Mathematics, 105(1): 121–139. doi:10.2307/1971028
  • –––, 2009, Subsystems of Second Order Arithmetic, second edition, (Perspectives in Logic), Cambridge: Cambridge University Press. doi:10.1017/CBO9780511581007
  • Singh, Parmanand, 1985, “The So-Called Fibonacci Numbers in Ancient and Medieval India”, Historia Mathematica, 12(3): 229–244. doi:10.1016/0315-0860(85)90021-7
  • Skolem, Thoralf, 1923, “Begründung Der Elementaren Arithmetik Durch Die Rekurrierende Denkweise Ohne Anwendung Scheinbarer Veranderlichen Mit Unendlichem Ausdehnungsbereich”, Videnskapsselskapets Skrifter, I. Matematisk-Naturvidenskabelig Klasse, 6: 1–38.
  • –––, 1946, “The development of recursive arithmetic” In Dixíeme Congrés des Mathimaticiens Scandinaves, Copenhagen, 1–16. Reprinted in Skolem 1970, pp. 499–415.
  • –––, 1970, Selected Works in Logic Olso: Universitetsforlaget. Edited by J.E. Fenstad.
  • Slaman, Theodore A., 2008, “Global Properties of the Turing Degrees and the Turing Jump”, in Computational Prospects of Infinity, by Chitat Chong, Qi Feng, Theodore A Slaman, W Hugh Woodin, and Yue Yang, (Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore 14), Singapore: World Scientific, 83–101. doi:10.1142/9789812794055_0002
  • Soare, Robert I., 1987, Recursively Enumerable Sets and Degrees: A Study of Computable Functions and Computably Generated Sets, Berlin: Springer.
  • –––, 1996, “Computability and Recursion”, Bulletin of Symbolic Logic, 2(3): 284–321. doi:10.2307/420992
  • –––, 2016, Turing Computability: Theory and Applications, Berlin: Springer. doi:10.1007/978-3-642-31933-4
  • Spector, Clifford, 1955, “Recursive Well-Orderings”, Journal of Symbolic Logic, 20(2): 151–163. doi:10.2307/2266902
  • Sudan, G., 1927, “Sur Le Nombre Transfinite \(\omega^{\omega}\)”, Bulletin Mathématique de La Société Roumaine Des Sciences, 30(1): 11–30.
  • Suslin, Michel, 1917, “Sur Une Définition Des Ensembles Mesurables sans Nombres Transfinis”, Comptes Rendus de l’Académie Des Sciences, 164(2): 88–91. (Scholar)
  • Tait, W. W., 1981, “Finitism”, The Journal of Philosophy, 78(9): 524–546. doi:10.2307/2026089
  • Tarski, Alfred, 1935, “Der Wahrheitsbegriff in den formalisierten Sprachen”, Studia Philosophica, 1: 261–405.
  • Tarski, Alfred, Andrzej Mostowski, and Raphael M. Robinson, 1953, Undecidable Theories, (Studies in Logic and the Foundations of Mathematics), Amsterdam: North-Holland.
  • Thomason, S. K., 1971, “Sublattices of the Recursively Enumerable Degrees”, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik/Mathematical Logic Quarterly, 17(1): 273–280. doi:10.1002/malq.19710170131
  • Turing, Alan M., 1937, “On Computable Numbers, with an Application to the Entscheidungsproblem”, Proceedings of the London Mathematical Society, s2-42(1): 230–265. doi:10.1112/plms/s2-42.1.230
  • –––, 1939, “Systems of Logic Based on Ordinals”, Proceedings of the London Mathematical Society, s2-45(1): 161–228. doi:10.1112/plms/s2-45.1.161
  • Wang, Hao, 1957, “The Axiomatization of Arithmetic”, Journal of Symbolic Logic, 22(2): 145–158. doi:10.2307/2964176
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