A generalized kleene-moschovakis theorem

Leo Harrington; Lefteris Kirousis; John Schlipf

doi:10.1090/S0002-9939-1978-0476457-5

A generalized kleene-moschovakis theorem

Leo Harrington, Lefteris Kirousis, John Schlipf

Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

Moschovakis generalized a theorem of Kleene to prove that if X is a collection of subsets of any acceptable structure m such that (m, K) ⊫ Δ¹1 comprehension, every hyperelementary subset of m is in k. We prove an analogous result for arbitrary m. We also get analogous results for m with an extra quantifier Q.

Original language	English (US)
Pages (from-to)	209-213
Number of pages	5
Journal	Proceedings of the American Mathematical Society
Volume	68
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-1978-0476457-5
State	Published - Feb 1978

Keywords

Admissible set
Deterministic-q-hyperelementary
Hyperelementary
Nonacceptable structure
Q_Hyperelementary
Strongly q-admissible set
Weakly q-admissible set
Δ1 comprehension

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-1978-0476457-5

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title = "A generalized kleene-moschovakis theorem",

abstract = "Moschovakis generalized a theorem of Kleene to prove that if X is a collection of subsets of any acceptable structure m such that (m, K) ⊫ Δ11 comprehension, every hyperelementary subset of m is in k. We prove an analogous result for arbitrary m. We also get analogous results for m with an extra quantifier Q.",

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AB - Moschovakis generalized a theorem of Kleene to prove that if X is a collection of subsets of any acceptable structure m such that (m, K) ⊫ Δ11 comprehension, every hyperelementary subset of m is in k. We prove an analogous result for arbitrary m. We also get analogous results for m with an extra quantifier Q.

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KW - Nonacceptable structure

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KW - Weakly q-admissible set

KW - Δ1 comprehension

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A generalized kleene-moschovakis theorem

Abstract

Keywords

ASJC Scopus subject areas

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