Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
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?)


Similar Articles

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

Retrieve articles in all journals with MSC: 02F27


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0476457-5
PII: S 0002-9939(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