  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
${\cal S}$-Ramsey subsets of $2^{\infty}\times {\cal R}$ is closed under the
Souslin operation. {\bf Key words and phrases}: Ramsey theorem, Ramsey space,
parametrization.
