We use the kernel category to give a finiteness condition for semigroups. As a consequence we provide yet another proof that finitely generated periodic semigroups of matrices are finite.

This thesis contributes to the study of families of finitely presented infinite graphs,their structural properties and their relations to each other. Given a finite alpha-bet Σ, a Σ-labeled infinite graph can be characterized as a finite set of binaryrelations (Ra)a∈Σ over an arbitrary countable domain V . There are many ways tofinitely characterize such sets of relations, eithe...

Abstract A left orderable monster is a finitely generated group all of whose fixed point-free actions on the line are proximal : action semiconjugate to minimal so that for every bounded interval I and open J , there element sends into . In his 2018 ICM address, Navas asked about existence monsters. By now several examples, which but not presentable. We provide first examples monsters presentab...

In this paper we study the structure of finitely presented Heyting algebras. Using algebraic techniques (as opposed to techniques from proof-theory) we show that every such Heyting algebra is in fact coHeyting, improving on a result of Ghilardi who showed that Heyting algebras free on a finite set of generators are co-Heyting. Along the way we give a new and simple proof of the finite model pro...