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

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 ♣-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
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DOI 10.1016/0168-0072(95)00040-2
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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.

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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.

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