arXiv subjects
Publications and source records attributed to Dimitris Vlitas.
We prove that for every equivalence relation on a barrier on the space $\langle FIN^{[\infty]}_k,\leq,r\rangle$, for any $k$, there exists $Y\in FIN_k^{[\infty]}$ so that the restriction of the coloring on $\langle Y\rangle$ is canonical.
In \cite{To} S. Todorcevic introduced the notion of a topological Ramsey space and a list of axioms required to be satisfied by any such a space. Here we show that any topological Ramsey space that satisfies a strengthened version of one of the required axioms and a very natural assumption, admits canonization theorem.
In this paper we complete the attempt of H. Lefmann to show that Borel equivalence relations on the $n$-element subsets of $2^ω$, that respect an order type, have a finite Ramsey basis.
Extending a result of K. Milliken \cite{Mi2}, in this paper we prove a Ramsey classification result for equivalence relations defined on uniform families of finite strong subtrees of a finite sequence $(U_i)_{i\in d}$ of fixed trees $U_i$, $i\in d$, that have a finite uniform branching but are of infinite length.
In a recent 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}.