We state the Ramsey property of classes of ordered structures with closures and given local properties. This generalises many old and new results: the Nešetřil-Rödl Theorem, the author’s Ramsey lift of bowtiefree graphs as well as the Ramsey Theorem for Finite Models (i.e. structures with both functions and relations) thus providing the ultimate generalisation of Structural Ramsey Theorem. We g...

Motivated by Tukey classification problems and building on work in Part 1 [5], we develop a new hierarchy of topological Ramsey spaces Rα, α < ω1. These spaces form a natural hierarchy of complexity, R0 being the Ellentuck space [7], and for each α < ω1, Rα+1 coming immediately after Rα in complexity. Associated with each Rα is an ultrafilter Uα, which is Ramsey for Rα, and in particular, is a ...

Motivated by Tukey classification problems and building on work in [4], we develop a new hierarchy of topological Ramsey spaces Rα, α < ω1. These spaces form a natural hierarchy of complexity, R0 being the Ellentuck space [6], and for each α < ω1, Rα+1 coming immediately afterRα in complexity. Associated with each Rα is an ultrafilter Uα, which is Ramsey for Rα, and in particular, is a rapid p-...

Parity automata are a generalisation of Büchi automata that have some interesting advantages over the latter, e.g. determinisability, succinctness and the ability to express certain acceptance conditions like the intersection of a Büchi and a co-Büchi condition directly as a parity condition. Decision problems like universality and inclusion for such automata are PSPACE-complete and have origin...

It is reasonably well-known in model theory that expansions of countable countablycategorical structures are closely associated with certain compactly metrizable spaces and, further, that a generic orbit in such a space – in the sense of Baire category – corresponds to an expansion with a particularly well-behaved model theory (relative to the base structure). Results of this kind can be found ...