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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
DOI: https://doi.org/10.1090/S0002-9939-1978-0476457-5
MathSciNet review: 0476457
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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] K. Jon Barwise, Admissible sets and structures, Springer-Verlag, Berlin and New York. MR 0424560 (54:12519)
  • [76] Admissible sets and monotone quantifiers, Lecture notes, U.C.L.A., spring 1976 (unpublished).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 (46:36)
  • [76] K. Jon Barwise and John Schlipf, On recursively saturated models of arithmetic, Model Theory and Algebra: A Memorial Tribute to Abraham Robinson, D. H. Saracino and B. Weispfenning (Editors), Lecture Notes in Math., vol. 498, Springer-Verlag, Berlin, pp. 42-54. MR 0409172 (53:12934)
  • [74] Y. N. Moschovakis, Elementary induction on abstract structures, North-Holland, Amsterdam. MR 0540769 (58:27486)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0476457-5
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

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