Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 54, Number 2 (2013), 125-136.
Consecutive Singular Cardinals and the Continuum Function
We show that from a supercompact cardinal , there is a forcing extension that has a symmetric inner model in which holds, and are both singular, and the continuum function at can be precisely controlled, in the sense that the final model contains a sequence of distinct subsets of of length equal to any predetermined ordinal. We also show that the above situation can be collapsed to obtain a model of in which either (1) and are both singular and the continuum function at can be precisely controlled, or (2) and are both singular and the continuum function at can be precisely controlled. Additionally, we discuss a result in which we separate the lengths of sequences of distinct subsets of consecutive singular cardinals and in a model of . Some open questions concerning the continuum function in models of with consecutive singular cardinals are posed.
Notre Dame J. Formal Logic, Volume 54, Number 2 (2013), 125-136.
First available in Project Euclid: 21 February 2013
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 03E25: Axiom of choice and related propositions
Secondary: 03E35: Consistency and independence results 03E45: Inner models, including constructibility, ordinal definability, and core models 03E55: Large cardinals
Apter, Arthur W.; Cody, Brent. Consecutive Singular Cardinals and the Continuum Function. Notre Dame J. Formal Logic 54 (2013), no. 2, 125--136. doi:10.1215/00294527-1960434. https://projecteuclid.org/euclid.ndjfl/1361454970