Instances of dependent choice and the measurability of אω + 1

Arthur W. Apter; Menachem Magidor

doi:10.1016/0168-0072(94)00039-6

Instances of dependent choice and the measurability of א_{ω + 1}

Arthur W. Apter^*
, Menachem Magidor

^*Corresponding author for this work

Einstein Institute of Mathematics

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

6 Scopus citations

Abstract

Starting from cardinals κ < λ where κ is 2^λ supercompact and λ > κ is measurable, we construct a model for the theory "ZF + ∀n < ω[DC_{א_n}] + א_{ω + 1} is a measurable cardinal". This is the maximum amount of dependent choice consistent with the measurability of א_{ω + 1}, and by a theorem of Shelah using p.c.f. theory, is the best result of this sort possible.

Original language	English
Pages (from-to)	203-219
Number of pages	17
Journal	Annals of Pure and Applied Logic
Volume	74
Issue number	3
DOIs	https://doi.org/10.1016/0168-0072(94)00039-6
State	Published - 18 Aug 1995

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AB - Starting from cardinals κ < λ where κ is 2λ supercompact and λ > κ is measurable, we construct a model for the theory "ZF + ∀n < ω[DCאn] + אω + 1 is a measurable cardinal". This is the maximum amount of dependent choice consistent with the measurability of אω + 1, and by a theorem of Shelah using p.c.f. theory, is the best result of this sort possible.

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Instances of dependent choice and the measurability of א_{ω + 1}

Abstract

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