Chang's conjecture may fail at supercompact cardinals (submitted)

Bernhard Koenig

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Chang's conjecture may fail at supercompact cardinals (submitted)

Bernhard Koenig

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Abstract

We prove a revised version of Laver's indestructibility theorem which slightly improves over the classical result. An application yields the consistency of $(κ^+,κ)\notcc(\aleph\_1,\aleph\_0)$ when $κ$ is supercompact. The actual proofs show that $ω\_1$-regressive Kurepa-trees are consistent above a supercompact cardinal even though ${\rm MM}$ destroys them on all regular cardinals. This rather paradoxical fact contradicts the common intuition.

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BibTeX RIS

Bernhard Koenig. 2006-05-04. Chang's conjecture may fail at supercompact cardinals (submitted). https://arxiv.org/abs/math/0605128

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