The set of equational classes of finitary functions on a finite set as a profinite semigroup
 
 
Description:  For a fixed finite set A, we consider sets of finitary functions (or operations) on A, henceforth called classes. We are interested in such classes that can be defined by certain functional equations. It turns out that they constitute a semigroup under the natural notion of class composition. The purpose of this talk is to report on recent joint work with M. Couceiro and T. Waldhauser on the structure of this semigroup. The interest in this work stems from its connections with multi-valued logic: for instance, its idempotents are the clones on A. In particular, it turns out to be a profinite semigroup under a natural metric defined in terms of the so-called essential arity. We have also obtained a description of its regular D-classes in the Boolean case, that is when A is a two-element set.
Date:  2014-01-09
Start Time:   14:30
Speaker:  Jorge Almeida (CMUP, Univ. Porto)
Institution:  CMUP, Universidade do Porto
Place:  Sala 5.5
Research Groups: -Algebra, Logic and Topology
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