Reflecting stationary sets

Journal of Symbolic Logic 47 (4):755-771 (1982)
  Copy   BIBTEX

Abstract

We prove that the statement "For every pair A, B, stationary subsets of ω 2 , composed of points of cofinality ω, there exists an ordinal α such that both A ∩ α and $B \bigcap \alpha$ are stationary subsets of α" is equiconsistent with the existence of weakly compact cardinal. (This completes results of Baumgartner and Harrington and Shelah.) We also prove, assuming the existence of infinitely many supercompact cardinals, the statement "Every stationary subset of ω ω + 1 has a stationary initial segment."

Other Versions

No versions found

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 101,880

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Reflecting stationary sets and successors of singular cardinals.Saharon Shelah - 1991 - Archive for Mathematical Logic 31 (1):25-53.
Stationary sets added when forcing squares.Maxwell Levine - 2018 - Archive for Mathematical Logic 57 (7-8):909-916.
Splitting stationary sets in.Toshimichi Usuba - 2012 - Journal of Symbolic Logic 77 (1):49-62.
Full reflection of stationary sets below ℵω.Thomas Jech & Saharon Shelah - 1990 - Journal of Symbolic Logic 55 (2):822 - 830.
Full reflection at a measurable cardinal.Thomas Jech & Jiří Witzany - 1994 - Journal of Symbolic Logic 59 (2):615-630.
Semistationary and stationary reflection.Hiroshi Sakai - 2008 - Journal of Symbolic Logic 73 (1):181-192.
Stationary Subsets of $\lbrack \aleph\omega \rbrack^{<\omegan}$.Kecheng Liu - 1993 - Journal of Symbolic Logic 58 (4):1201 - 1218.
Adding a Nonreflecting Weakly Compact Set.Brent Cody - 2019 - Notre Dame Journal of Formal Logic 60 (3):503-521.
Possible PCF algebras.Thomas Jech & Saharon Shelah - 1996 - Journal of Symbolic Logic 61 (1):313-317.

Analytics

Added to PP
2009-01-28

Downloads
77 (#275,376)

6 months
13 (#281,088)

Historical graph of downloads
How can I increase my downloads?

References found in this work

Strong axioms of infinity and elementary embeddings.Robert M. Solovay - 1978 - Annals of Mathematical Logic 13 (1):73.
A new class of order types.James E. Baumgartner - 1976 - Annals of Mathematical Logic 9 (3):187-222.
The fine structure of the constructible hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.
Boolean extensions and measurable cardinals.K. Kunen - 1971 - Annals of Mathematical Logic 2 (4):359.

Add more references