# Elementary and non-elementary inclusive varieties

`2024-05-08 10:30:00``2024-05-08 11:30:00``Elementary and non-elementary inclusive varieties``The class of identical inclusions was defined by E. S. Lyapin. This is a class of universal formulas which is situated strictly between identities and universal positive formulas. These universal formulas can be written as identical equalities of subsets of words: elements of the free semigroup. Classes of semigroups defined by identical inclusions are called inclusive varieties. The language of identical inclusions is much richer than the language of identities; for example, there are infinitely many semigroups defined by identical inclusions up to isomorphism and there exist infinitely many countable inclusive varieties of semigroups. Many basic classes of semigroups (finite groups, p-groups, Engel groups, solvable groups, nilsemigroups, nilpotent semigroups, periodic Clifford semigroups) are non-elementary inclusive varieties, i.e. they are inclusive varieties that cannot be defined by sets of first-order formulas. After an introduction, I plan to speak about non-elementary inclusive varieties. In particular, I will give a criterion for an inclusive variety to be non-elementary. I plan to speak also about inclusive varieties of abelian groups and, if time allows, about inclusive varieties of Clifford semigroups. ================================================ https://us02web.zoom.us/j/87856132062 Meeting ID: 878 5613 2062``Third floor seminar room and Zoom``אוניברסיטת בר-אילן - Department of Mathematics``mathoffice@math.biu.ac.il``Asia/Jerusalem``public`The class of identical inclusions was defined by E. S. Lyapin. This is a class of universal formulas which is situated strictly between identities and universal positive formulas. These universal formulas can be written as identical equalities of subsets of words: elements of the free semigroup. Classes of semigroups defined by identical inclusions are called inclusive varieties. The language of identical inclusions is much richer than the language of identities; for example, there are infinitely many semigroups defined by identical inclusions up to isomorphism and there exist infinitely many countable inclusive varieties of semigroups. Many basic classes of semigroups (finite groups, p-groups, Engel groups, solvable groups, nilsemigroups, nilpotent semigroups, periodic Clifford semigroups) are non-elementary inclusive varieties, i.e. they are inclusive varieties that cannot be defined by sets of first-order formulas.

After an introduction, I plan to speak about non-elementary inclusive varieties. In particular, I will give a criterion for an inclusive variety to be non-elementary. I plan to speak also about inclusive varieties of abelian groups and, if time allows, about inclusive varieties of Clifford semigroups.

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https://us02web.zoom.us/j/87856132062

Meeting ID: 878 5613 2062

Last Updated Date : 06/05/2024