TY - JOUR
T1 - Saturated filters at successors of singulars, weak reflection and yet another weak club principle
AU - Džamonja, Mirna
AU - Shelah, Saharon
PY - 1996/6/24
Y1 - 1996/6/24
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0030600018&partnerID=8YFLogxK
U2 - 10.1016/0168-0072(95)00025-9
DO - 10.1016/0168-0072(95)00025-9
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AN - SCOPUS:0030600018
SN - 0168-0072
VL - 79
SP - 221
EP - 280
JO - Annals of Pure and Applied Logic
JF - Annals of Pure and Applied Logic
IS - 3
ER -