Saturated filters at successors of singulars, weak reflection and yet another weak club principle

Mirna Džamonja*, Saharon Shelah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

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 Clubsuit sign-principle, which we call Clubsuit sign*-, 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, Clubsuit sign*-(S) 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 Clubsuit sign*-(S) holds modulo an ideal obtained through the weak reflection.

Original languageEnglish
Pages (from-to)221-280
Number of pages60
JournalAnnals of Pure and Applied Logic
Volume79
Issue number3
DOIs
StatePublished - 24 Jun 1996

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