A characterization of tolerance-distributive tree semilattices
A characterization of varieties of inverse semigroups.
A classification of rational languages by semilattice-ordered monoids
We prove here an Eilenberg type theorem: the so-called conjunctive varieties of rational languages correspond to the pseudovarieties of finite semilattice-ordered monoids. Taking complements of members of a conjunctive variety of languages we get a so-called disjunctive variety. We present here a non-trivial example of such a variety together with an equational characterization of the corresponding pseudovariety.
A clone-theoretic formulation of the Erdos-Faber-Lovász conjecture
The Erdős-Faber-Lovász conjecture states that if a graph G is the union of n cliques of size n no two of which share more than one vertex, then χ(G) = n. We provide a formulation of this conjecture in terms of maximal partial clones of partial operations on a set.
A common generalization of permutability and 0-permutability
A concept of variety for regular biordered sets.
A contribution to the theory of decompositions of partial algebras
A counterexample in the cohomology of monoids.
A deceptive fact about functions
The paper provides a proof of a combinatorial result which pertains to the characterization of the set of equations which are solvable in the composition monoid of all partial functions on an infinite set.
A deductive calculus for conditional equational systems with built-in predicates as premises.
A dichotomy theorem for mono-unary algebras
We study the isomorphism relation of invariant Borel classes of countable mono-unary algebras and prove a strong dichotomy theorem.
A duality between infinitary varieties and algebraic theories
A duality between -ary varieties and -ary algebraic theories is proved as a direct generalization of the finitary case studied by the first author, F.W. Lawvere and J. Rosick’y. We also prove that for every uncountable cardinal , whenever -small products commute with -colimits in , then must be a -filtered category. We nevertheless introduce the concept of -sifted colimits so that morphisms between -ary varieties (defined to be -ary, regular right adjoints) are precisely the functors...
A duality between unary algebras and their subuniverse lattices
A duality for isotropic median algebras
We establish categorical dualities between varieties of isotropic median algebras and suitable categories of operational and relational topological structures. We follow a general duality theory of B.A. Davey and H. Werner. The duality results are used to describe free isotropic median algebras. If the number of free generators is less than five, the description is detailed.
A dyadic view of rational convex sets
Let be a subfield of the field of real numbers. Equipped with the binary arithmetic mean operation, each convex subset of becomes a commutative binary mode, also called idempotent commutative medial (or entropic) groupoid. Let and be convex subsets of . Assume that they are of the same dimension and at least one of them is bounded, or is the field of all rational numbers. We prove that the corresponding idempotent commutative medial groupoids are isomorphic iff the affine space ...
A factorization of quasiorder hypergroups
The contribution is devoted to the question of the interchange of the construction of a quasiorder hypergroup from a quasiordered set and the factorization.
A finite axiomatization of nondeterministic regular expressions
A Finite Axiomatization of Nondeterministic Regular Expressions
An alternative (tree-based) semantics for a class of regular expressions is proposed that assigns a central rôle to the + operator and thus to nondeterminism and nondeterministic choice. For the new semantics a consistent and complete axiomatization is obtained from the original axiomatization of regular expressions by Salomaa and by Kozen by dropping the idempotence law for + and the distribution law of • over +.
A first-order logic for multi-algebras.
A functional characterization of parallelogram spaces