Atomic compactness and elementary equivalence
Atomicity of tolerance lattices
Atomicity of tolerance lattices of commutative semigroups
Atomistic congruence lattices of semilattices.
Atomless Parts of Spaces.
Automorphism Groups of Finite Distributive Lattices with a Given Sublattice of Fixed Points.
Automorphisms of categories of free algebras of varieties.
Axiomatization of quasigroups
Quasigroups were originally described combinatorially, in terms of existence and uniqueness conditions on the solutions to certain equations. Evans introduced a universal-algebraic characterization, as algebras with three binary operations satisfying four identities. Now, quasigroups are redefined as heterogeneous algebras, satisfying just two conditions respectively known as hypercommutativity and hypercancellativity.
Axiomatizing omega and omega-op powers of words
In 1978, Courcelle asked for a complete set of axioms and rules for the equational theory of (discrete regular) words equipped with the operations of product, omega power and omega-op power. In this paper we find a simple set of equations and prove they are complete. Moreover, we show that the equational theory is decidable in polynomial time.
Axiomatizing omega and omega-op powers of words
In 1978, Courcelle asked for a complete set of axioms and rules for the equational theory of (discrete regular) words equipped with the operations of product, omega power and omega-op power. In this paper we find a simple set of equations and prove they are complete. Moreover, we show that the equational theory is decidable in polynomial time.