Journal of Symbolic Logic

Determinacy in strong cardinal models

P. D. Welch

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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.

Article information

Source
J. Symbolic Logic, Volume 76, Issue 2 (2011), 719-728.

Dates
First available in Project Euclid: 19 May 2011

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1305810772

Digital Object Identifier
doi:10.2178/jsl/1305810772

Mathematical Reviews number (MathSciNet)
MR2830424

Zentralblatt MATH identifier
1221.03055

Citation

Welch, P. D. Determinacy in strong cardinal models. J. Symbolic Logic 76 (2011), no. 2, 719--728. doi:10.2178/jsl/1305810772. https://projecteuclid.org/euclid.jsl/1305810772


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