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.

The minimum weight of a nowhere first-countable compact space of countable π-weight is shown to be κB, the least cardinal κ for which the real line R can be covered by κ many nowhere dense sets.

Let H be a countable infinite homogeneous relational structure. If H is indivisible then it is weakly indivisible and if it is weakly indivisible then it is age indivisible. There are examples of countable infinite homogeneous structures which are weakly indivisible but not indivisible. It is a natural question to ask for examples of countable age indivisible homogenous structures which are not...