Instances of dependent choice and the measurability of ℵω + 1

Annals of Pure and Applied Logic 74 (3):203-219 (1995)
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Abstract

Starting from cardinals κ κ is measurable, we construct a model for the theory “ZF + n < ω[DCn] + ω + 1 is a measurable cardinal”. This is the maximum amount of dependent choice consistent with the measurability of ω + 1, and by a theorem of Shelah using p.c.f. theory, is the best result of this sort possible

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References found in this work

A combinatorial property of p κλ.Telis K. Menas - 1976 - Journal of Symbolic Logic 41 (1):225-234.
Some applications of model theory in set theory.Jack H. Silver - 1971 - Annals of Mathematical Logic 3 (1):45.
Successors of singular cardinals and measurability revisited.Arthur W. Apter - 1990 - Journal of Symbolic Logic 55 (2):492-501.
An AD-Like model.Arthur W. Apter - 1985 - Journal of Symbolic Logic 50 (2):531-543.

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