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Ad and patterns of singular cardinals below θ
Journal of Symbolic Logic 61 (1):225-235 (1996)
Abstract
Using Steel's recent result that assuming AD, in L[R] below Θ, κ is regular $\operatorname{iff} \kappa$ is measurable, we mimic below Θ certain earlier results of Gitik. In particular, we construct via forcing a model in which all uncountable cardinals below Θ are singular and a model in which the only regular uncountable cardinal below Θ is ℵ 1Links
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Citations of this work
The first measurable cardinal can be the first uncountable regular cardinal at any successor height.Arthur W. Apter, Ioanna M. Dimitriou & Peter Koepke - 2014 - Mathematical Logic Quarterly 60 (6):471-486.
The strength of choiceless patterns of singular and weakly compact cardinals.Daniel Busche & Ralf Schindler - 2009 - Annals of Pure and Applied Logic 159 (1-2):198-248.
The Consistency Strength of $$\aleph{\omega}$$ and $$\aleph_{{\omega}1}$$ Being Rowbottom Cardinals Without the Axiom of Choice.Arthur W. Apter & Peter Koepke - 2006 - Archive for Mathematical Logic 45 (6):721-737.
Consecutive Singular Cardinals and the Continuum Function.Arthur W. Apter & Brent Cody - 2013 - Notre Dame Journal of Formal Logic 54 (2):125-136.
On the Consistency Strength of Two Choiceless Cardinal Patterns.Arthur W. Apter - 1999 - Notre Dame Journal of Formal Logic 40 (3):341-345.
References found in this work
Strong axioms of infinity and elementary embeddings.Robert M. Solovay - 1978 - Annals of Mathematical Logic 13 (1):73.
Some new upper bounds in consistency strength for certain choiceless large cardinal patterns.Arthur W. Apter - 1992 - Archive for Mathematical Logic 31 (3):201-205.
Some strong axioms of infinity incompatible with the axiom of constructibility.Frederick Rowbottom - 1971 - Annals of Mathematical Logic 3 (1):1.
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