Информационная система "Конференции"

Abstracts

Non-classical logics, proof theory and universal algebra

On lattices of Equational Theories We shall say that $I$ is an equational theory if $I$ is a set of identities closed under deduction. Let $L(I)$=${Т: I in Т and T is an equational theory}$. In 1945 G.Birkhoff and in 1965 A.I.Malcev posed problem of characterizing those lattices that can be isomorphic to an $L(I)$. We shall construct class $M$ of monoids with additional two unary operations such that a lattice $L$ is isomorphic to lattice of equational theory $I$ iff $L$ is isomorphic to congruence lattice of some algebra $M(I)$ belonging to $M$. As corollary we obtain that $I$ is decidable iff $M(I)$ has solvable word problem and $I$ is finitely based iff $M(I)$ is finitely represented into class $M$.

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