Journal of Symbolic Logic 68 (4):1163-1170 (2003)

Authors
Abstract
A classic result of Baumgartner-Harrington-Kleinberg [1] 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 $\omega_2^L$ is countable: { $X \in L \mid X \subseteq \omega_1^L$ and X has a CUB subset in a cardinal -preserving extension of L} is constructible, as it equals the set of constructible subsets of $\omega_1^L$ which in L are stationary. Is there a similar such result for subsets of $\ omega_2^L$ ? Building on work of M. Stanley [9], 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
Keywords Descriptive set theory   large cardinals   innermodels
Categories (categorize this paper)
DOI 10.2178/jsl/1067620178
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 55,873
Through your library

References found in this work BETA

The Fine Structure of the Constructible Hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.

Add more references

Citations of this work BETA

Adding Closed Unbounded Subsets of Ω₂ with Finite Forcing.William J. Mitchell - 2005 - Notre Dame Journal of Formal Logic 46 (3):357-371.
Forcing Closed Unbounded Subsets of Ω2.M. C. Stanley - 2001 - Annals of Pure and Applied Logic 110 (1-3):23-87.

Add more citations

Similar books and articles

Jónsson Cardinals, Erdös Cardinals, and the Core Model.W. J. Mitchell - 1999 - Journal of Symbolic Logic 64 (3):1065-1086.
Characterising Subsets of Ω1 Constructible From a Real.P. D. Welch - 1994 - Journal of Symbolic Logic 59 (4):1420 - 1432.
Forcing Isomorphism II.M. C. Laskowski & S. Shelah - 1996 - Journal of Symbolic Logic 61 (4):1305-1320.
Full Reflection at a Measurable Cardinal.Thomas Jech & Jiří Witzany - 1994 - Journal of Symbolic Logic 59 (2):615-630.
Spector Forcing.J. M. Henle - 1984 - Journal of Symbolic Logic 49 (2):542-554.
Co-Stationarity of the Ground Model.Natasha Dobrinen & Sy-David Friedman - 2006 - Journal of Symbolic Logic 71 (3):1029 - 1043.
Reflecting Stationary Sets.Menachem Magidor - 1982 - Journal of Symbolic Logic 47 (4):755-771.

Analytics

Added to PP index
2009-01-28

Total views
23 ( #448,029 of 2,401,775 )

Recent downloads (6 months)
1 ( #551,897 of 2,401,775 )

How can I increase my downloads?

Downloads

My notes