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Transversals for strongly almost disjoint families

Authors:	Paul J Szeptycki

Institution:	Department of Mathematics and Statistics, York University, Toronto, OntarioCanada M3J 1P3

Abstract:	For a family of sets , and a set , is said to be a transversal of if $X\subseteq \bigcup A$ and $\vert a\cap X\vert=1$ for each $a\in A$ . is said to be a Bernstein set for if $\emptyset\not=a\cap X\not=a$ for each $a\in A$ . Erdos and Hajnal first studied when an almost disjoint family admits a set such as a transversal or Bernstein set. In this note we introduce the following notion: a family of sets is said to admit a $\sigma$ -transversal if can be written as $A=\bigcup\{A_n:n\in \omega\}$ such that each admits a transversal. We study the question of when an almost disjoint family admits a $\sigma$ -transversal and related questions.

Keywords:	Almost disjoint family transversal Bernstein partition

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