Recursive functionals and quantifiers of finite types. I
HTML articles powered by AMS MathViewer
- by S. C. Kleene PDF
- Trans. Amer. Math. Soc. 91 (1959), 1-52 Request permission
References
-
L. E. J. Brouwer, Beweis, dass jede volle Funktion gleichmässig stetig ist, Nederl. Akad. Wetensch. vol. 27 (1924) pp. 189-193.
- L. E. J. Brouwer, Über Definitionsbereiche von- Funktionen, Math. Ann. 97 (1927), no. 1, 60–75 (German). MR 1512354, DOI 10.1007/BF01447860 —, Points and spaces, Canad. J. Math. vol. 6 (1953) pp. 1-17.
- Alonzo Church, An Unsolvable Problem of Elementary Number Theory, Amer. J. Math. 58 (1936), no. 2, 345–363. MR 1507159, DOI 10.2307/2371045 M. Davis, On the theory of recursive unsolvability, Ph.D. thesis (typewritten), Princeton University, 1950.
- Andrzej Grzegorczyk, Some classes of recursive functions, Rozprawy Mat. 4 (1953), 46. MR 60426
- A. Grzegorczyk, Computable functionals, Fund. Math. 42 (1955), 168–202. MR 86756, DOI 10.4064/fm-42-1-168-202
- S. C. Kleene, General recursive functions of natural numbers, Math. Ann. 112 (1936), no. 1, 727–742. MR 1513071, DOI 10.1007/BF01565439
- S. C. Kleene, A note on recursive functions, Bull. Amer. Math. Soc. 42 (1936), no. 8, 544–546. MR 1563352, DOI 10.1090/S0002-9904-1936-06353-6
- S. C. Kleene, Recursive predicates and quantifiers, Trans. Amer. Math. Soc. 53 (1943), 41–73. MR 7371, DOI 10.1090/S0002-9947-1943-0007371-8
- S. C. Kleene, On the forms of the predicates in the theory of constructive ordinals, Amer. J. Math. 66 (1944), 41–58. MR 9757, DOI 10.2307/2371894
- S. C. Kleene, Recursive functions and intuitionistic mathematics, Proceedings of the International Congress of Mathematicians, Cambridge, Mass., 1950, vol. 1, Amer. Math. Soc., Providence, R.I., 1952, pp. 679–685. MR 0044468
- Stephen Cole Kleene, Introduction to metamathematics, D. Van Nostrand Co., Inc., New York, N. Y., 1952. MR 0051790
- S. C. Kleene, Arithmetical predicates and function quantifiers, Trans. Amer. Math. Soc. 79 (1955), 312–340. MR 70594, DOI 10.1090/S0002-9947-1955-0070594-4
- S. C. Kleene, On the forms of the predicates in the theory of constructive ordinals. II, Amer. J. Math. 77 (1955), 405–428. MR 70595, DOI 10.2307/2372632
- S. C. Kleene, Hierarchies of number-theoretic predicates, Bull. Amer. Math. Soc. 61 (1955), 193–213. MR 70593, DOI 10.1090/S0002-9904-1955-09896-3 —, Extension of an effectively generated class of functions by enumeration, Colloquium Mathematicum (Wrocław), vol. 6. —, Countable functionals, Constructivity in Mathematics, Amsterdam, North-Holland.
- S. C. Kleene and Emil L. Post, The upper semi-lattice of degrees of recursive unsolvability, Ann. of Math. (2) 59 (1954), 379–407. MR 61078, DOI 10.2307/1969708 D. König, Über eine Schlussweise aus dem Endlichen ins Unendliche, Acta Sci. Math. Szeged vol. 3 (1927) pp. 121-130. G. Kreisel, Constructive interpretations of analysis by means of functionals of finite type, Constructivity in Mathematics, Amsterdam, North-Holland. R. Péter, Über den Zusammenhang der verschiedenen Begriffe der rekursiven Funktion, Math. Ann. vol. 110 (1934) pp. 612-632.
- Rózsa Péter, Rekursive Funktionen, Akademischer Verlag, Budapest, 1951 (German). MR 0044467
- Rózsa Péter, Probleme der Hilbertschen Theorie der höheren Stufen von rekursiven Funktionen, Acta Math. Acad. Sci. Hungar. 2 (1951), 247–274 (German, with Russian summary). MR 53042, DOI 10.1007/BF02020732 E. L. Post, Degrees of recursive unsolvability (Preliminary report), Bull. Amer. Math. Soc. Abstract 54-7-269.
- Clifford Spector, Recursive well-orderings, J. Symbolic Logic 20 (1955), 151–163. MR 74347, DOI 10.2307/2266902
- Clifford Spector, On degrees of recursive unsolvability, Ann. of Math. (2) 64 (1956), 581–592. MR 82457, DOI 10.2307/1969604
- Alfred Tarski, Einige Betrachtungen über die Begriffe der $\omega$-Widerspruchsfreiheit und der $\omega$-Vollständigkeit, Monatsh. Math. Phys. 40 (1933), no. 1, 97–112 (German). MR 1550192, DOI 10.1007/BF01708855
- Alfred Tarski, A problem concerning the notion of definability, J. Symbolic Logic 13 (1948), 107–111. MR 26625, DOI 10.2307/2267331 A. M. Turing, Systems of logic based on ordinals, Proc. London Math. Soc. (2) vol. 45 (1939) pp. 161-228.
Additional Information
- © Copyright 1959 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 91 (1959), 1-52
- MSC: Primary 02.00
- DOI: https://doi.org/10.1090/S0002-9947-1959-0102480-9
- MathSciNet review: 0102480