Combinatorics on Ideals and Axiom A

Details Combinatorics on Ideals and Axiom A Combinatorics on Ideals and Axiom A

1993-02-26

arxiv.org/abs/math/9302203v1

Mathematics

Logic

Scientific paper

Throughout this abstract let U be a fixed p-point ultrafilter and let I be the dual ideal. Grigorieff forcing is P(U)={p:omega to 2|dom(p) is an element of I} ordered by reverse inclusion. It is well known that Grigorieff forcing is proper. The main result of this paper is the following: THEOREM: Gregorieff forcing does not satisfy Axiom A. To prove this we use the following game, denoted G(U), for two players playing alternatively: Player I plays a partition of omega, {J_n| n

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