A parametrization of the abstract Ramsey theorem

Abstract

We give a parametrization with perfect subsets of $2^{\infty }$ of the abstract Ramsey theorem (see \cite{todo}) Our main tool is an extension of the parametrized version of the combinatorial forcing developed in \cite{nash} and \cite{todo}, used in \cite{mij} to the obtain a parametrization of the abstract Ellentuck theorem. As one of the consequences, we obtain a parametrized version of the Hales-Jewett theorem. Finally, we conclude that the family of perfectly $\mathcal{S}$-Ramsey subsets of $2^{\infty }\times \mathcal{R}$ is closed under the Souslin operation. {\bf Key words and phrases}: Ramsey theorem, Ramsey space, parametrization.

14 pages

References in corpus (1)

• Parametrizing the abstract Ellentuck theorem