抽象Ramsey定理的参数化
A parametrization of the abstract Ramsey theorem
摘要：
我们给出了一个参数化的完美子集的$2^{\infty}$的抽象拉姆齐定理（见\cite{todo}）我们的主要工具是一个扩展的参数化版本的组合迫使在\cite{nash}和\cite{todo}，用于在\cite{mij}获得参数化的抽象埃伦塔克定理。作为结果之一，我们得到一个参数化版本的Hales-Jewett定理。最后，我们得出结论：$2^{\infty}\times {\cal R}$的完全${\cal S}$-Ramsey子集族在Souslin运算下是闭的. { \bf关键词}：拉姆齐定理，拉姆齐空间，参数化。
英文摘要：
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.
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