Annals of Pure and Applied Logic 79 (3):289-316 (1996)

Suppose that λ is the successor of a singular cardinal μ whose cofinality is an uncountable cardinal κ. We give a sufficient condition that the club filter of λ concentrating on the points of cofinality κ is not λ+-saturated.1 The condition is phrased in terms of a notion that we call weak reflection. We discuss various properties of weak reflection. We introduce a weak version of the ♣-principle, which we call ♣*−, and show that if it holds on a stationary subset S of λ, then no normal filter on S is λ+-saturated. Under the above assumptions, ♣*− is true for any stationary subset S of λ which does not contain points of cofinality κ. For stationary sets S which concentrate on points of cofinality κ, we show that ♣*− holds modulo an ideal obtained through the weak reflection
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1016/0168-0072(95)00040-2
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: 53,013
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Reflecting Stationary Sets and Successors of Singular Cardinals.Saharon Shelah - 1991 - Archive for Mathematical Logic 31 (1):25-53.
Saturated Ideals.Kenneth Kunen - 1978 - Journal of Symbolic Logic 43 (1):65-76.
A New Class of Order Types.James E. Baumgartner - 1976 - Annals of Mathematical Logic 9 (3):187-222.
Diamonds, Uniformization.Saharon Shelah - 1984 - Journal of Symbolic Logic 49 (4):1022-1033.

Add more references

Citations of this work BETA

A Relative of the Approachability Ideal, Diamond and Non-Saturation.Assaf Rinot - 2010 - Journal of Symbolic Logic 75 (3):1035-1065.
Operations, Climbability and the Proper Forcing Axiom.Yasuo Yoshinobu - 2013 - Annals of Pure and Applied Logic 164 (7-8):749-762.
On Guessing Generalized Clubs at the Successors of Regulars.Assaf Rinot - 2011 - Annals of Pure and Applied Logic 162 (7):566-577.

Add more citations

Similar books and articles

Weak Measurement and Weak Information.Boaz Tamir & Sergei Masis - 2012 - Foundations of Physics 42 (4):531-543.
Infinitary Combinatorics and Modal Logic.Andreas Blass - 1990 - Journal of Symbolic Logic 55 (2):761-778.
Finding Generic Filters by Playing Games.Heike Mildenberger - 2010 - Archive for Mathematical Logic 49 (1):91-118.
On Some Configurations Related to the Shelah Weak Hypothesis.Moti Gitik & Saharon Shelah - 2001 - Archive for Mathematical Logic 40 (8):639-650.
The Weak Pigeonhole Principle for Function Classes in S12.Norman Danner & Chris Pollett - 2006 - Mathematical Logic Quarterly 52 (6):575-584.
Club Guessing Sequences and Filters.Tetsuya Ishiu - 2005 - Journal of Symbolic Logic 70 (4):1037-1071.
A Relative of the Approachability Ideal, Diamond and Non-Saturation.Assaf Rinot - 2010 - Journal of Symbolic Logic 75 (3):1035-1065.
A Note on Weak Dividing.Byunghan Kim & Niandong Shi - 2007 - Archive for Mathematical Logic 46 (2):51-60.
Reverse Mathematics and a Ramsey-Type König's Lemma.Stephen Flood - 2012 - Journal of Symbolic Logic 77 (4):1272-1280.
Weak and Global Supervenience Are Strong.Mark Moyer - 2008 - Philosophical Studies 138 (1):125 - 150.
Weak-Operator Continuity and the Existence of Adjoints.Douglas Bridges & Luminita Dediu - 1999 - Mathematical Logic Quarterly 45 (2):203-206.


Added to PP index

Total views
7 ( #973,139 of 2,344,162 )

Recent downloads (6 months)
1 ( #514,058 of 2,344,162 )

How can I increase my downloads?


My notes