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In issues bearing on the structure of universal algebras , derived structures, such as automorphism groups Aut , subalgebra lattices Sub , congruence lattices Con , etc., play an important part. On the other hand, in studying universal algebras by the means of model theory, of crucial importance...
Let qG be a quasivariety generated by a group G and be a non-Abelian quasivariety of groups with a finite lattice of subquasivarieties. Suppose is contained in a quasivariety generated by the following two groups: a free 2-nilpotent group F 2 ( 2 ) of rank 2 and a free metabelian (i.e., with an...
We examine some many-modal logics extending S5 t , t ∈ N, for decidability w.r.t. admissibility of inference rules, and for the logics in question, we prove an algorithmic criterion determining whether the inference rules in them are admissible.
Various types of lattices are embedded in suborder lattices of posets possessing certain properties. In particular, it is shown that the class of lattices isomorphic to sublattices of suborder lattices of posets of length at most n is a variety, for any n < ω.
In (6), a complete description was furnished for ℵ 0 -categorical o-minimal theories. That description implies that these theories are binary. We give a description for ℵ 0 -categorical, binary, weakly o-minimal theories of convexity rank 1.
The statement “no non-Abelian simple group can be obtained from a non-simple one by adding one generator and one relator” first is equivalent to the Kervaire-Laudenbach conjecture, and second, becomes true under the additional assumption that an initial non-simple group is either finite or...
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