An Infinite self dual Ramsey theorem

Abstract: In a paper \cite{So} S. Solecki proves a finite self dual Ramsey theorem that in a natural way gives simultaneously the classical finite Ramsey theorem \cite{Ra} and the Graham-Rothschild theorem \cite{Gr-Ro}. In this paper we prove the corresponding infinite dimensional self dual theorem, giving similarly as a consequence the infinite classical Ramsey theorem \cite{Ra} and the Carlson-Simpson theorem \cite{Ca-Si}.