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Determinacy in strong cardinal models

Published online by Cambridge University Press:  12 March 2014

P. D. Welch
P. D. Welch*
Affiliation:
School of Mathematics, University of Bristol, Bristol, BS8 1TW, UK, E-mail: p.welch@bristol.ac.uk
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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(-IND) ⇒ there exists an inner model with a strong cardinal.

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

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

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 2 , June 2011 , pp. 719 - 728
Copyright
Copyright © Association for Symbolic Logic 2011

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References

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