Parametrizing the abstract Ellentuck theorem

Details Parametrizing the abstract Ellentuck theorem Parametrizing the abstract Ellentuck theorem

2005-10-21

arxiv.org/abs/math/0510477v1

Discrete Mathematics, Volume 307, Issue 2, January 2007, 216-225

Mathematics

Logic

16 pages. Submitted to Elsevier's Discrete Mathematics

Scientific paper

10.1016/j.disc.2006.06.022

We give a parametrization with perfect sets of the abstract Ellentuck theorem. The main tool for achieving this goal is a sort of parametrization of an abstract version of the Nash-Williams theorem. As corollaries, we obtain some known classical results like the parametrized version of the Galvin-Prikry theorem due to Miller and Todorcevic, and the parametrized version of Ellentuck's theorem due to Pawlikowski. Also, we obtain parametized vesions of nonclassical results such as Milliken's theorem.

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