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RELATIVIZING OPERATIONAL SET THEORY

Published online by Cambridge University Press:  10 October 2016

GERHARD JÄGER
GERHARD JÄGER*
Affiliation:
GERHARD JÄGER, INSTITUT FÜR INFORMATIK UNIVERSITÄT BERN, NEUBRÜCKSTRASSE 10 CH-3012 BERN, SWITZERLAND E-mail: jaeger@inf.unibe.ch
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Abstract

We introduce a way of relativizing operational set theory that also takes care of application. After presenting the basic approach and proving some essential properties of this new form of relativization we turn to the notion of relativized regularity and to the system OST (LR) that extends OST by a limit axiom claiming that any set is element of a relativized regular set. Finally we show that OST (LR) is proof-theoretically equivalent to the well-known theory KPi for a recursively inaccessible universe.

Keywords

03B3003B4003E2003F03operational set theoryKripke–Platek set theoryproof theory

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Type
Articles
Information
Bulletin of Symbolic Logic , Volume 22 , Issue 3 , September 2016 , pp. 332 - 352
Copyright
Copyright © The Association for Symbolic Logic 2016 

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