Prof. Tommaso Moraschini (University of Barcelona) will give a seminar on Thursday 15 May 2025 at 11:30 in Sala Riunioni, DipMat.
Title: Implicit operations in algebra and logic.
Abstract: It is well known that the partial operation of taking inverses in monoids is preserved under homomorphisms and, moreover, is definable by a first-order formula in the language of monoids. Operations of this kind—definable and preserved by homomorphisms—will be called implicit operations. Since implicit operations may go beyond the language of the class of algebras under consideration (as in the case of inverses in monoids), it is natural to ask whether such operations can be interpolated by actual terms in the original language. Remarkably, the requirement that all implicit operations in a quasivariety K be interpolable by terms is equivalent to a strong form of the epimorphism surjectivity property in K. In this talk, we will develop the theory of implicit operations and interpolability from the perspectives of universal algebra and algebraic logic. This is joint work with Luca Carai and Miriam Kurtzhals.
0 Comments