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Ágnes Szendrei (University of Boulder): Idempotent Linear Maltsev Conditions: Can We Find Interesting Models by Random Search?

 Wednesday, 5. June 2019, 10:00 - 11:00

Abstract.

Let L be a finite algebraic language with at least one operation symbol of arity >1. By a result of Murskii (1975), a random finite L-algebra is almost surely a semiprimal algebra with no proper subalgebras of size >1. In a recent joint paper with Cliff Bergman (2018+) we looked at the analogous problem when the probability space is restricted to the class of all finite models of a set M of idempotent linear L-identities, i.e., the identities of a strong, idempotent, linear Maltsev condition. We found a simple syntactic condition (*) such that M satisfies (*) if and only if a random finite model of M is almost surely idemprimal.

I will start the talk by reviewing this result, and then I will discuss the following question: Which clones occur with positive probability among the clones of random finite models of M? Clearly, this question is interesting only if (*) fails for M; this is the case, for example, if M is the set of identities for a Maltsev term, or majority term, or minority term, or semiprojection term.
Location : Bolyai Intézet, I. emelet, Riesz terem, Aradi vértanúk tere 1., Szeged