Tommaso Moraschini (University of Barcelona) will give a talk on
Epimorphisms surjectivity between finitely generated algebras
Abstract:
This talk is based on joint work with Luca Carai and Miriam Kurtzhals. A quasivariety K is said to have the weak epimorphism surjectivity property (weak ES property, for short) when all the epimorphisms between finitely generated members of K are surjective. From a logical standpoint, the interest of the weak ES property is motivated as follows: when a quasivariety K algebraizes a logic L, the former has the weak ES property iff the latter has the Beth definability property (which, roughly, means that every implicit definition in L can be turned explicit). In general, the task of determining whether a quasivariety has the weak ES property is nontrivial and our results facilitate the detection of failures of the weak ES property. Furthermore, we will show that the weak ES property has a profound influence on the structure theory of the quasivariety under consideration. These results have been collected here.