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June 2012 The stable core
Sy-David Friedman
Bull. Symbolic Logic 18(2): 261-267 (June 2012). DOI: 10.2178/bsl/1333560807

Abstract

Vopenka [2] proved long ago that every set of ordinals is set-generic over HOD, Gödel's inner model of hereditarily ordinal-definable sets. Here we show that the entire universe V is class-generic over (HOD,S), and indeed over the even smaller inner model $\mathbb{S}=(L[S],S)$, where S is the Stability predicate. We refer to the inner model $\mathbb{S}$ as the Stable Core of V. The predicate S has a simple definition which is more absolute than any definition of HOD; in particular, it is possible to add reals which are not set-generic but preserve the Stable Core (this is not possible for HOD by Vopenka's theorem).

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Sy-David Friedman. "The stable core." Bull. Symbolic Logic 18 (2) 261 - 267, June 2012. https://doi.org/10.2178/bsl/1333560807

Information

Published: June 2012
First available in Project Euclid: 4 April 2012

zbMATH: 1258.03071
MathSciNet: MR2931674
Digital Object Identifier: 10.2178/bsl/1333560807

Rights: Copyright © 2012 Association for Symbolic Logic

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Vol.18 • No. 2 • June 2012
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