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

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

2006-05-04

arxiv.org/abs/math/0605128v1

Mathematics

Logic

Scientific paper

We prove a revised version of Laver's indestructibility theorem which slightly improves over the classical result. An application yields the consistency of $(\kappa^+,\kappa)\notcc(\aleph\_1,\aleph\_0)$ when $\kappa$ is supercompact. The actual proofs show that $\omega\_1$-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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