Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A generalized Kleene-Moschovakis theorem

Authors: Leo Harrington, Lefteris Kirousis and John Schlipf
Journal: Proc. Amer. Math. Soc. 68 (1978), 209-213
MSC: Primary 02F27
MathSciNet review: 0476457
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Moschovakis generalized a theorem of Kleene to prove that if $ \mathfrak{X}$ is a collection of subsets of any acceptable structure $ \mathfrak{M}$ such that $ (\mathfrak{M},\mathfrak{X}) \vDash \Delta _1^1$ comprehension, every hyperelementary subset of $ \mathfrak{M}$ is in $ \mathfrak{X}$. We prove an analogous result for arbitrary $ \mathfrak{M}$. We also get analogous results for $ \mathfrak{M}$ with an extra quantifier Q.

References [Enhancements On Off] (What's this?)

  • [75] Jon Barwise, Admissible sets and structures, Springer-Verlag, Berlin-New York, 1975. An approach to definability theory; Perspectives in Mathematical Logic. MR 0424560
  • [76] Admissible sets and monotone quantifiers, Lecture notes, U.C.L.A., spring 1976 (unpublished).
  • [71] K. J. Barwise, R. O. Gandy, and Y. N. Moschovakis, The next admissible set, J. Symbolic Logic 36 (1971), 108–120. MR 0300876
  • [76] Jon Barwise and John Schlipf, On recursively saturated models of arithmetic, Model theory and algebra (A memorial tribute to Abraham Robinson), Springer, Berlin, 1975, pp. 42–55. Lecture Notes in Math., Vol. 498. MR 0409172
  • [74] Y. N. Moschovakis, Analytical definability in a playful universe, Logic, methodology and philosophy of science, IV (Proc. Fourth Internat. Congr., Bucharest, 1971) North-Holland, Amsterdam, 1973, pp. 77–85. Studies in Logic and Foundations of Math., Vol. 74. MR 0540769

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 02F27

Retrieve articles in all journals with MSC: 02F27

Additional Information

Keywords: Admissible set, weakly Q-admissible set, strongly Q-admissible set, hyperelementary, Q-hyperelementary, deterministic-Q-hyperelementary, $ \Delta _1^1$ comprehension, nonacceptable structure
Article copyright: © Copyright 1978 American Mathematical Society