Relativizing operational set theory

Bulletin of Symbolic Logic 22 (3):332-352 (2016)
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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 that extends OST by a limit axiom claiming that any set is element of a relativized regular set. Finally we show that OST is proof-theoretically equivalent to the well-known theory KPi for a recursively inaccessible universe.

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10.1017/bsl.2016.11

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A well-ordering proof for Feferman's theoryT 0.Gerhard Jäger - 1983 - Archive for Mathematical Logic 23 (1):65-77.
On Feferman’s operational set theory OST.Gerhard Jäger - 2007 - Annals of Pure and Applied Logic 150 (1-3):19-39.
Operational closure and stability.Gerhard Jäger - 2013 - Annals of Pure and Applied Logic 164 (7-8):813-821.
About the Strength of Operational Regularity.Gerhard Jäger & Rico Zumbrunnen - 2012 - In Ulrich Berger, Hannes Diener, Peter Schuster & Monika Seisenberger (eds.), Logic, Construction, Computation. De Gruyter. pp. 305-324.

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