1,063 research outputs found
Club-guessing, stationary reflection, and coloring theorems
We obtain strong coloring theorems at successors of singular cardinals from
failures of certain instances of simultaneous reflection of stationary sets.
Along the way, we establish new results in club-guessing and in the general
theory of ideals.Comment: Initial public versio
Saturated filters at successors of singulars, weak reflection and yet another weak club principle
Suppose that lambda is the successor of a singular cardinal mu whose
cofinality is an uncountable cardinal kappa. We give a sufficient condition
that the club filter of lambda concentrating on the points of cofinality kappa
is not lambda^+-saturated. The condition is phrased in terms of a notion that
we call weak reflection. We discuss various properties of weak reflectio
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