June 2011 Determinacy in strong cardinal models
P. D. Welch
J. Symbolic Logic 76(2): 719-728 (June 2011). DOI: 10.2178/jsl/1305810772

Abstract

We give limits defined in terms of abstract pointclasses of the amount of determinacy available in certain canonical inner models involving strong cardinals. We show for example:

Theorem A. Det(Π¹₁-IND) → there exists an inner model with a strong cardinal.

Theorem B. Det(AQI) → there exist type-1 mice and hence inner models with proper classes of strong cardinals.

where Π¹₁-IND(AQI) is the pointclass of boldface Π¹₁-inductive (respectively arithmetically quasi-inductive) sets of reals.

Citation

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P. D. Welch. "Determinacy in strong cardinal models." J. Symbolic Logic 76 (2) 719 - 728, June 2011. https://doi.org/10.2178/jsl/1305810772

Information

Published: June 2011
First available in Project Euclid: 19 May 2011

zbMATH: 1221.03055
MathSciNet: MR2830424
Digital Object Identifier: 10.2178/jsl/1305810772

Rights: Copyright © 2011 Association for Symbolic Logic

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Vol.76 • No. 2 • June 2011
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