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Definability in the lattice of equational theories of semigroups
We study first-order definability in the latticeL of equational theories of semigroups. A large collection of individual theories and some interesting sets of theories are definable inL. As examples,Expand
Definability in Substructure Orderings, II: Finite Ordered Sets
It is shown that every isomorphism-invariant relation between finite posets that is definable in a certain strongly enriched second-order language is first-order definable up to duality in the ordered set p. Expand
Equational theories of medial groupoids
Finitely generated algebraic structures with various divisibility conditions
Abstract. Infinite fields are not finitely generated rings. A similar question is considered for further algebraic structures, mainly commutative semirings. In this case, purely algebraic methodsExpand
Intervals in the lattice of varieties
Subdirectly irreducible semilattices with an automorphism
In other words, SA is the variety of semilattices with one automorphism (which is, as well as its inverse, considered as an additional fundamental operation). The aim of this paper is to find allExpand
Minimal varieties and quasivarieties of semilattices with one automorphism
We describe all minimal quasivarieties and all minimal varieties of semilattices with one automorphism (considered as algebras with one binary and two unary operations).