The lattice of equational theories. Part IV: Equational theories of finite algebras

Equational Logic and Equational Theories of Algebras

Lattices of Equational Theories as Church Algebras

We introduce the class of Church algebras, which is general enough to compass all Boolean algebras, Heyting algebras and rings with unit. Using a new equational characterization of central elements, we prove that Church algebras satisfy a Stone representation theorem. We show that every lattice of equational theories is isomorphic to the congruence lattice of a suitable Church algebra, and we u...

Finite Model Search for Equational Theories (FMSET)

Finite model and counter model generation is a potential alternative in automated theorem proving. In this paper, we introduce a system called FMSET which generates finite structures representing models of equational theories. FMSET performs a satisfiability test over a set of special first order clauses called ”simple clauses”. Several experiments over a variety of problems have been pursued. ...

Definability in the lattice of equational theories of semigroups

We study first-order definability in the lattice L of equational theories of semigroups. A large collection of individual theories and some interesting sets of theories are definable in L . As examples, if T is either the equational theory of a finite semigroup or a finitely axiomatizable locally finite theory, then the set {T, T } is definable, where T ∂ is the dual theory obtained by invertin...

Definability in the Lattice of Equational Theories of Commutative Semigroups

In this paper we study first-order definability in the lattice of equational theories of commutative semigroups. In a series of papers, J. Ježek, solving problems posed by A. Tarski and R. McKenzie, has proved, in particular, that each equational theory is first-order definable in the lattice of equational theories of a given type, up to automorphism, and that such lattices have no automorphism...