Inductive definitions and computability-Reference-Cited by-同舟云学术

Inductive definitions and computability

Published:1971 Issue:2 Volume:158 Page:309-317
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Grilliot Thomas J.

Abstract

Sets inductively defined with respect to ∏ 0 , Σ 1 {\prod _0},{\Sigma _1} , (nonmonotonic) ∏ 1 {\prod _1} and Σ 2 {\Sigma _2} predicates are characterized in terms of the four chief notions of abstract recursion.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1971-158-02/S0002-9947-1971-0304141-5/S0002-9947-1971-0304141-5.pdf

Reference11 articles.

1. The next admissible set;Barwise, K. J.;J. Symbolic Logic,1971

2. R. Fraïssé, Une notion de récursivité relative, Proc. Sympos. Infinitistic Methods, Foundations of Math. (Warsaw, 1959), Pergamon Press, Oxford; PWN, Warsaw, 1961, pp. 323-328. MR 32 #3999.

3. C. E. Gordon, A comparison of abstract computability theories, J. Symbolic Logic 34 (1969), 156.

4. Selection functions for recursive functionals;Grilliot, Thomas J.;Notre Dame J. Formal Logic,1969

5. Deux généralisations de la notion de récursivité relative;Lacombe, Daniel;C. R. Acad. Sci. Paris,1964

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1. Bibliography;Studies in Logic and the Foundations of Mathematics;1992

2. The least α for which E(α) is inadmissible;Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics;1986-10

3. Recursion and Nonmonotone Induction in a Quantifier;The Kleene Symposium;1980

4. Spector Second Order Classes and Reflection;Studies in Logic and the Foundations of Mathematics;1978

5. On recursion in $$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{E}$$ and semi-spector classes;Lecture Notes in Mathematics;1978