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The theory of recursive functions, approaching its centennial
Author(s):
Stephen C.
Kleene
Journal:
Bull. Amer. Math. Soc.
5
(1981),
43-61.
MSC (1980):
Primary 03D20;
Secondary 03D10, 03A05
Corrigendum:
Bull. Amer. Math. Soc. (N.S.), Volume 5, Number 3 (1981), 364--364
MathSciNet review:
614313
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References:
- Ackermann, Wilhelm, [1928] Zum Hilbertschen Aufbau der reellen Zahlen, Math. Ann. 99, 118-133. MR 1512441
- Cantor, Georg, [1874] Über eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen, J. Reine Angew. Math. 77, 258-262.
- Cantor, Georg, [1895-7] Beiträge zur Begründung der transfiniten Mengenlehre, Math. Ann. 46 (1895), 481-512; 49 (1897), 207-246. MR 1510964
- Church, Alonzo, [1932] A set of postulates for the foundation of logic, Ann. of Math. (2) 33, 346-366. MR 1503059
- Church, Alonzo, [1933] A set of postulates for the foundation of logic (second paper), Ann. of Math. (2) 34, 839-864. MR 1503136
- Church, Alonzo, [1936] An unsolvable problem of elementary number theory, Amer. J. Math. 58, 345-363. MR 1507159
- Church, Alonzo, [1936a] A note on the Entscheidungsproblem, J. Symbolic Logic 1, 40-41; Correction, 101-102. MR 441682
- Dedekind, Richard, [1888] Was sind und was sollen die Zahlen? Braunschweig.
- Gödel, Kurt, [1931] Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme. I, Monatsh. Math. Phys. 38, 173-198. MR 1549910
- Gödel, Kurt, [1934] On undecidable propositions of formal mathematical systems, mimeographed notes by S. C. Kleene and J. B. Rosser on lectures at the Institute for Advanced Study, 1934; reprinted in Martin Davis, The undecidable, basic papers on undecidable propositions, unsolvable problems and computable functions, Raven Press, Hewlett, N. Y., 1965, pp. 39-74. MR 2070909
- Hilbert, David, [1918] Axiomatisches Denken, Math. Ann. 78, 405-415. MR 1511909
- Hilbert, David, [1926] Über das Unendliche, Math. Ann. 95, 161-190. MR 1512272
- Kleene, Stephen, C., [1935] A theory of positive integers in formal logic, Amer. J. Math. 57, 153-173; 219-244.
- Kleene, Stephen, C., [1936] General recursive functions of natural numbers, Math. Ann. 112, 727-742. MR 1513071
- Kleene, Stephen, C., [1936a] λ-definability and recursiveness, Duke Math. J. 2, 340-353. MR 1545927
- Kleene, Stephen, C., [ 1938] On notation for ordinal numbers, J. Symbolic Logic 3, 150-155.
- Kleene, Stephen, C., [1943] Recursive predicates and quantifiers, Trans. Amer. Math. Soc. 53, 41-73. MR 7371
- Kleene, Stephen, C., [1950] Recursive functions and intuitionistic mathematics, Proc. Internat. Congr. Math. (Cambridge, Mass., U.S.A., 1950), Amer Math. Soc., Providence, R. I., 1952, I, pp. 679-685. MR 44468
- Kleene, Stephen, C., [1952] Introduction to metamathematics, North-Holland, Amsterdam, P. Noordhoff, Groningen and D. Van Nostrand, Toronto and New York. MR 51790
- Kleene, Stephen, C., [1955] Arithmetical predicates and function quantifiers, Trans. Amer. Math. Soc. 79, 312-340. MR 70594
- Kleene, Stephen, C., [1955a] On the forms of the predicates in the theory of constructive ordinals (second paper), Amer. J. Math. 77, 405-428. MR 70595
- Kleene, Stephen, C., [1955b] Hierarchies of number-theoretic predicates, Bull. Amer. Math. Soc. 61, 193-213. MR 70593
- Kleene, Stephen, C., [1957] Mathematics, foundations of, Encyclopaedia Britannica, 1957 and subsequent printings. Beginning with 1974, the article was reworked to replace Kleene's section on intuitionism by a fuller treatment by Solomon Fefermann.
- Kleene, Stephen, C., [1958] Mathematical logic: constructive and non-constructive operations, Proc. Internat. Congr. Math. (Edinburgh, 1958) (J. A. Todd, ed.), Cambridge at the University Press, 1960, pp. 137-153. MR 114750
- Kleene, Stephen, C., [1959] Recursive functionals and quantifiers of finite types. I, Trans. Amer. Math. Soc. 91, 1-52. MR 102480
- Kleene, Stephen, C., [1963] Recursive functionals and quantifiers of finite types. II, Trans. Amer. Math. Soc. 108, 106-142. MR 153557
- Kleene, Stephen, C., [1964] Computability, The Voice of America Forum Lectures, Phil. of Science Series, no. 6; reprinted, Philosophy of Science Today (Sidney Morgenbesser, ed.), Basic Books, New York and London, 1967, pp. 36-45.
- Kleene, Stephen, C., [1967] Mathematical logic, Wiley, New York, London and Sidney. MR 216930
- Kleene, Stephen, C., [1969] The new logic, Sigma-Xi-RESA National Lecture, Southeast Tour (Spring 1969), Amer. Sci. 57, 333-347.
- Kleene, Stephen, C., [1978] Recursive functionals and quantifiers of finite types revisited. I. Generalized Recursion Theory. II, Proc. 1977 Oslo Sympos. (J. E. Fenstad, R. O. Gandy and G. E.Sacks, eds.), North-Holland, Amsterdam, New York and Oxford, pp. 185-222. MR 516936
- Kleene, Stephen, C., [1980] Recursive functionals and quantifiers of finite types revisited. II, The Kleene Symposium (Madison, Wis., June 1978) (J. Barwise, H. J. Keisler and K. Kunen, eds.), North-Holland, Ansterdam, New York and Oxford, pp. 1-29. MR 591873
- Kleene, Stephen, C., [1981a] Origins of recursive function theory, 20th Annual Sympos. Foundations of Computer Science (San Juan, Puerto Rico, 1979), Institute of Electrical and Electronics Engineers (IEEE 79CH 1471-2C), pp. 371-382; Annals of the History of Computing, 1981 (to appear). MR 598119
- Kleene, Stephen, C., [1981b] Algorithms in various contexts, Proc. Sympos. Algorithms in Modern Mathematics and Computer Science (dedicated to Al-Khowarizmi) (Urgench, Khorezm Region, Uzbek, SSSR, 1979), Springer-Verlag, Berlin, Heidelberg and New York, 1981 (to appear). MR 657625
- Klein, Felix, [1908-9] Elementarmathematik vom höheren Standpunkte aus, Lithographed, Leipzig; English transl. from 3rd German ed. (E. R. Hedrick and C. A. Noble, eds.), Macmillan, New York, 1932.
- Kronecker, Leopold, [1886] The saying quoted in the third paragraph of the text was spoken in his lecture on 21 September 1886 before der Deutschen Naturforscherversammlung zu Berlin, according to H. Weber, Leopold Kronecker, Math. Ann. 43 (1893), 1-25 (cf. p. 15). Also cf. Leopold Kronecker's Werke, hrg. K. Henzel, vol. 3, pt. 2, p. 203.
- Löwenheim, Leopold, [1915] Über Möglichkeiten im Relativkalkül, Math. Ann. 76, 447-470. MR 1511835
- Marcov, A. A., [1951] Theory of algorithms, Amer. Math. Soc. Transl. (2) 15 (1960), 1-14. MR 114753
- Marcov, A. A., [1954] Theory of algorithms, The National Science Foundation, Washington, D.C., the Department of Commerce, U.S.A., and the Israel Program for Scientific Translation, Jerusalem, 1961. MR 132690
- Peano, Guiseppe, [1889] Arithmetices principia, nova methodo exposita, Turin, Bocca.
- Peano, Guiseppe, [1891] Sul concetto di numero, Rivista di Matematica 1, 87-102; 256-267.
- Péter, Rózsa, [1934] Über den Zusammenhang der verschiedenen Begriffe der rekursiven Funktion, Math. Ann. 110, 612-632. MR 1512957
- Péter, Rózsa, [1935] Konstruktion nichtrekursiver Funktionen, Math. Ann. 111, 42-60. MR 1512975
- Péter, Rózsa, [1935] Über die mehrfache Rekursion, Math. Ann. 113, 489-527. MR 1513105
- Post, Emil L., [1936] Finite combinatory processes-formulation 1, J. Symbolic Logic 1, 103-105. MR 20527
- Post, Emil L., [1943] Formal reductions of the general combinatorial decision problem, Amer. J. Math. 65, 197-215. MR 7893
- Post, Emil L., [1944] Recursively enumerable sets of positive integers and their decision problems, Bull. Amer. Math. Soc. 50, 284-316. MR 10514
- Post, Emil L., [1948] Degrees of recursive unsolvability, abstract (preliminary report) in Bull. Amer. Math. Soc. 54, 641-642.
- Schröder, Ernst, [1895] Vorlesungen über die Algebra der Logik (exakte Logik), 3 Algebra und Logik der Relative, part 1, Leipzig.
- Skolem, Thoralf, [1923] Begründung der elementaren Arithmetik durch die rekurrierende Denkweise ohne Anwendung scheinbare Veränderlichen mit unendlichem Ausdehnungsbereich, Skrifter utgit av Videnskapsselskapet i Kristiania, I. Matematisk-Naturvidenskabelig Klasse 1923, no. 6; English transl., Jean van Heijenoort, From Frege to Gödel, a source book in mathematical logic, 1879-1931, Harvard Univ. Press, Cambridge, Mass., 1967, pp. 302-333.
- Smullyan, Raymond M., [1961] Theory of formal systems, Annals of Math. Studies, no. 47, Princeton Univ. Press, Princeton, N. J. MR 152429
- Turing, Allan Mathison, [1936-7] On computable numbers, with an application to the Entscheidungsproblem, Proc. London Math. Soc. (2) 42, 230-265; A Correction, 43 (1937), 544-546.
- Turing, Allan Mathison, [1939] Systems of logic based on ordinals, Proc. London Math. Soc. (2) 45, 161-228.
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Additional Information:
DOI:
10.1090/S0273-0979-1981-14920-X
PII:
S 0273-0979(1981)14920-X
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