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CHANG’S CONJECTURE, GENERIC ELEMENTARY EMBEDDINGS AND INNER MODELS FOR HUGE CARDINALS

Published online by Cambridge University Press:  15 September 2015

MATTHEW FOREMAN
MATTHEW FOREMAN*
Affiliation:
MATHEMATICS DEPARTMENT UC IRVINE IRVINE, CA, 92697-3875, USAE-mail: mforeman@math.uci.edu
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Abstract

We introduce a natural principle Strong Chang Reflection strengthening the classical Chang Conjectures. This principle is between a huge and a two huge cardinal in consistency strength. In this note we prove that it implies the existence of an inner model with a huge cardinal. The technique we explore for building inner models with huge cardinals adapts to show that decisive ideals imply the existence of inner models with supercompact cardinals. Proofs for all of these claims can be found in [10].1,2

Keywords

Chang’s Conjectureinner modelshuge cardinals
Type
Articles
Information
Bulletin of Symbolic Logic , Volume 21 , Issue 3 , September 2015 , pp. 251 - 269
Copyright
Copyright © The Association for Symbolic Logic 2015 

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