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 f inite L-algebra is almost surely a semiprimal algebra with no proper subalg ebras of size >1. In a recent joint paper with Cliff Bergman (2018+) we loo ked at the analogous problem when the probability space is restricted to th e 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 onl y if a random finite model of M is almost surely idemprimal.

I wil l start the talk by reviewing this result, and then I will discuss the foll owing question: Which clones occur with positive probability among the clon es 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 iden tities for a Maltsev term, or majority term, or minority term, or semiproje ction term. DTSTAMP:20200707T082346Z DTSTART;TZID=Europe/Budapest:20190605T100000 DTEND;TZID=Europe/Budapest:20190605T110000 SEQUENCE:0 TRANSP:OPAQUE END:VEVENT END:VCALENDAR