0# and Elementary end extensions of Vκ

Amir Leshem

doi:10.1090/s0002-9939-01-05847-6

0^# and Elementary end extensions of V_κ

Amir Leshem

Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we prove that if κ is a cardinal in L[0^#], then there is an inner model M such that M (V_κ, ε) has no elementary end extension. In particular if 0^# exists, then weak compactness is never downwards absolute. We complement the result with a lemma stating that any cardinal greater than N₁ of uncountable cofinality in L[0^#] is Mahlo in every strict inner model of L[0^#].

Original language	English
Pages (from-to)	2445-2450
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	129
Issue number	8
DOIs	https://doi.org/10.1090/s0002-9939-01-05847-6
State	Published - 2001
Externally published	Yes

Keywords

0
Inner models
Models of set theory

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10.1090/s0002-9939-01-05847-6

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0^# and Elementary end extensions of V_κ

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Keywords

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