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ABOUT SOME FIXED POINT AXIOMS AND RELATED PRINCIPLES IN KRIPKE–PLATEK ENVIRONMENTS

Published online by Cambridge University Press:  01 August 2018

GERHARD JÄGER  and
SILVIA STEILA
GERHARD JÄGER
Affiliation:
INSTITUT FÜR INFORMATIK, UNIVERSITÄT BERN NEUBRÜCKSTRASSE 10, CH-3012 BERN, SWITZERLANDE-mail:jaeger@inf.unibe.ch
SILVIA STEILA
Affiliation:
INSTITUT FÜR INFORMATIK, UNIVERSITÄT BERN NEUBRÜCKSTRASSE 10, CH-3012 BERN, SWITZERLANDE-mail:steila@inf.unibe.ch
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Abstract

Starting points of this article are fixed point axioms for set-bounded monotone Σ1 definable operators in the context of Kripke–Platek set theory $KP$. We analyze their relationship to other principles such as maximal iterations, bounded proper injections, and Σ1 subset-bounded separation. One of our main results states that in $KP + (V\, = \,L)$ all these principles are equivalent to Σ1 separation.

Keywords

03E3003F0303F25Kripke–Platek set theoryset-bounded Σ1 operatorsfixed point axiomsbounded proper Σ1 injectionsΣ1 separation and Σ1 subset-bounded separation
Type
Articles
Information
The Journal of Symbolic Logic , Volume 83 , Issue 2 , June 2018 , pp. 642 - 668
Copyright
Copyright © The Association for Symbolic Logic 2018 

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