Abstract

It is a theorem of Prikry [7] that ifκcarries a uniformη-descendingly complete ultrafilter then the stationary reflection propertyfails. In this paper we will derive similar results, but here from properties of filters rather than ultrafilters.Throughoutκandηwill denote regular cardinals withη<κ, andIwill denote an ideal onκ, by which we mean a setI⊆P such that Iis closed under taking subsets and finite unions and αЄIfor eachα<κ, butκ∉I.Iis said to beμ-complete if it is closed under taking unions of size <μ,I* = {X⊆κ∣κ−XЄI} is the filter dual toIand ifAЄI+ −I), thenI∣Ais the ideal onκgiven byI∣A= {X⊆κ∣X∩AЄI}. Ifh: A→κthenhis said to be unbounded modIif for eachα<κ,h−1 = {ξЄA∣h<α} ЄIand a least function forIifhis unbounded modIand wheneverg: A→κis a function, unbounded modI, then {ξЄA∣g{ξ)

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