We consider random processes more general than those considered by Erdös and Rényi for generating the countable random graph. It is proved that, in the category sense, almost all random processes we consider generate the countable random graph with probability 1. Under a weak boundedness assumption we give a criterion for the random processes which generate the countable random graph almost sur...

We consider topological dynamical systems ( X , T ) where is a compact metrizable space and denotes an action of countable amenable group G on by homeomorphisms. For two such Y S factor map π : → intermediate system Z R for which can be written as composition maps ψ φ . In this paper, we show that any -subshifts the set entropies subshift factors dense in interval [ h ] As corollary, also prove...

Abstract In this paper, we establish a connection between categorical closedness and nontopologizability of semigroups. particular, for the class

We construct a fully faithful functor from the category of graphs to the category of fields. Using this functor, we resolve a longstanding open problem in computable model theory, by showing that for every nontrivial countable structure S, there exists a countable field F with the same essential computable-model-theoretic properties as S. Along the way, we develop a new “computable category the...

In this paper, we prove the number of countable models of a countable supersimple theory is either 1 or infinite. This result is an extension of Lachlan’s theorem on a superstable theory.