Almost disjoint families and property (a)

Paul Szeptycki; Jerry Vaughan

ArticleOriginal scientific text

Title

Almost disjoint families and property (a)

Authors ¹, ²

Affiliations

Department of Mathematics, Ohio University, Athens, Ohio 45701, U.S.A.
Department of Mathematical Sciences, University of North Carolina at Greensboro, Greensboro, North Carolina 27412, U.S.A.

Abstract

We consider the question: when does a Ψ-space satisfy property (a)? We show that if

| A | < g o t p

then the Ψ-space Ψ(A) satisfies property (a), but in some Cohen models the negation of CH holds and every uncountable Ψ-space fails to satisfy property (a). We also show that in a model of Fleissner and Miller there exists a Ψ-space of cardinality

g o t p

which has property (a). We extend a theorem of Matveev relating the existence of certain closed discrete subsets with the failure of property (a).

Keywords

ENG

property (a), density, extent, almost disjoint families, Ψ-space, CH, GCH, Martin's Axiom,

g o t p = g o t c

, Cohen forcing, Q-set, weakly inaccessible cardinal.

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Title

Almost disjoint families and property (a)

Affiliations

Abstract

Keywords

Bibliography