Journal of Symbolic Logic

Cardinal-preserving extensions

Sy D. Friedman

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Abstract

A classic result of Baumgartner-Harrington-Kleinberg implies that assuming CH a stationary subset of ω1 has a CUB subset in a cardinal-perserving generic extension of V, via a forcing of cardinality ω1. Therefore, assuming that ω2L is countable: { X ∈ L | X⊆ ω1L and X has a CUB subset in a cardinal-preserving extension of L} is constructible, as it equals the set of constructible subsets of ω1L which in L are stationary. Is there a similar such result for subsets of ω2L? Building on work of M. Stanley, we show that there is not. We shall also consider a number of related problems, examining the extent to which they are “solvable” in the above sense, as well as defining a notion of reduction between them.

Article information

Source
J. Symbolic Logic, Volume 68, Issue 4 (2003), 1163-1170.

Dates
First available in Project Euclid: 31 October 2003

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1067620178

Digital Object Identifier
doi:10.2178/jsl/1067620178

Mathematical Reviews number (MathSciNet)
MR2017346

Zentralblatt MATH identifier
1059.03051

Subjects
Primary: 03E35: Consistency and independence results 03E45: Inner models, including constructibility, ordinal definability, and core models 03E55: Large cardinals

Keywords
Descriptive set theory large cardinals innermodels

Citation

Friedman, Sy D. Cardinal-preserving extensions. J. Symbolic Logic 68 (2003), no. 4, 1163--1170. doi:10.2178/jsl/1067620178. https://projecteuclid.org/euclid.jsl/1067620178


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References

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