Chang’s conjecture, generic elementary embeddings and inner models for huge cardinals

Bulletin of Symbolic Logic 21 (3):251-269 (2015)
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Abstract

We introduce a natural principleStrong Chang Reflectionstrengthening 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 thatdecisiveideals imply the existence of inner models with supercompact cardinals. Proofs for all of these claims can be found in [10].1,2.

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Citations of this work

In memoriam: James Earl Baumgartner (1943–2011).J. A. Larson - 2017 - Archive for Mathematical Logic 56 (7):877-909.

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References found in this work

Saturated ideals.Kenneth Kunen - 1978 - Journal of Symbolic Logic 43 (1):65-76.
Descriptive inner model theory.Grigor Sargsyan - 2013 - Bulletin of Symbolic Logic 19 (1):1-55.

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