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Pré-Publication, Document De Travail Année : 2006

Chang's conjecture may fail at supercompact cardinals

Bernhard Koenig
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Résumé

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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Dates et versions

hal-00023748 , version 1 (04-05-2006)

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Bernhard Koenig. Chang's conjecture may fail at supercompact cardinals. 2006. ⟨hal-00023748⟩
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