Some Game-Theoretic Characterizations for Rapid Filters on ω

Infinite game is a power tool in studying various objects and finding descriptions of some properties of filters in mathematics.Game-theoretic characterizations for meager filters,Q-filters and Ramsey filters were obtained by Tomek Bartoszynski,Claude Laflamme and Marion Scheepers.In this paper,the authors obtain two game-theoretic characterizations for rapid filters onω.

Selection Principles and Sierpinski Sets

We show that a set of real numbers is a Sierpinski set if, and only if, it satisfies a selection property similar to the familiar Menger property.