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DERIVED MODELS OF MICE BELOW THE LEAST FIXPOINT OF THE SOLOVAY SEQUENCE

Published online by Cambridge University Press:  07 February 2019

DOMINIK ADOLF  and
GRIGOR SARGSYAN
DOMINIK ADOLF
Affiliation:
DEPARTMENT OF MATHEMATICS RUTGERS UNIVERSITY PISCATAWAY, NJ08854-8018, USAE-mail: d_adol01@uni.muenster.de
GRIGOR SARGSYAN
Affiliation:
DEPARTMENT OF MATHEMATICS RUTGERS UNIVERSITY PISCATAWAY, NJ08854-8018, USAE-mail: grigor@math.rutgers.edu
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Abstract

We introduce a mouse whose derived model satisfies $AD_ + {\rm{\Theta }} \ge \theta _{\aleph _2 } $. More generally, we will introduce a class of large cardinal properties yielding mice whose derived models can satisfy properties as strong as $AD_ + {\rm{\Theta }} = \theta _{\rm{\Theta }} $.

Keywords

03E4503E60derived modelsmiceSolovay sequence
Type
Articles
Information
The Journal of Symbolic Logic , Volume 84 , Issue 1 , March 2019 , pp. 27 - 53
Copyright
Copyright © The Association for Symbolic Logic 2019 

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