An algebraic and logical approach to continuous images
An algebraic completeness proof for Kleene's 3-valued logic
We introduce Kleene's 3-valued logic in a language containing, besides the Boolean connectives, a constant for the undefined truth value, so in developing semantics we can switch from the usual treatment based on DM-algebras to the narrower class of DMF-algebras (De Morgan algebras with a single fixed point for negation). A sequent calculus for Kleene's logic is introduced and proved complete with respect to threevalent semantics. The completeness proof is based on a version of the prime ideal...
An algebraic treatment of flow diagrams and its application to generalized recursion theory
An algebraic version of the Cantor-Bernstein-Schröder theorem
The Cantor-Bernstein-Schröder theorem of the set theory was generalized by Sikorski and Tarski to -complete boolean algebras, and recently by several authors to other algebraic structures. In this paper we expose an abstract version which is applicable to algebras with an underlying lattice structure and such that the central elements of this lattice determine a direct decomposition of the algebra. Necessary and sufficient conditions for the validity of the Cantor-Bernstein-Schröder theorem for...
An algorithm to compute the möbius function of the rotation lattice of binary trees
An analogue of covering space theory for ranked posets.
An analogue of the Krein-Milman theorem for star-shaped sets.
An analysis of GCD and LCM matrices via the -factorization.
An application of soft sets to lattices
An approach to a dual of regular closure operators
An approach to covering dimensions
Using certain ideas connected with the entropy theory, several kinds of dimensions are introduced for arbitrary topological spaces. Their properties are examined, in particular, for normal spaces and quasi-discrete ones. One of the considered dimensions coincides, on these spaces, with the Čech-Lebesgue dimension and the height dimension of posets, respectively.
An approach to solvability in orthomodular lattices
An atomic MV-effect algebra with non-atomic center
Does there exist an atomic lattice effect algebra with non-atomic subalgebra of sharp elements? An affirmative answer to this question (and slightly more) is given: An example of an atomic MV-effect algebra with a non-atomic Boolean subalgebra of sharp or central elements is presented.
An embedding problem and its application in linguistics
An equational basis in four variables for the three-element tournament
An equivalence between varieties of cyclic Post algebras and varieties generated by a finite field
In this paper we give a term equivalence between the simple k-cyclic Post algebra of order p, L p,k, and the finite field F(p k) with constants F(p). By using Lagrange polynomials, we give an explicit procedure to obtain an interpretation Φ1 of the variety V(L p,k) generated by L p,k into the variety V(F(p k)) generated by F(p k) and an interpretation Φ2 of V(F(p k)) into V(L p,k) such that Φ2Φ1(B) = B for every B ε V(L p,k) and Φ1Φ2(R) = R for every R ε V(F(p k)).
An equivalency problem in discrete programming over ordered semigroups.
An extension of the Stone representation for orthomodular lattices
An extension theorem for modular measures on effect algebras
We prove an extension theorem for modular measures on lattice ordered effect algebras. This is used to obtain a representation of these measures by the classical ones. With the aid of this theorem we transfer control theorems, Vitali-Hahn-Saks, Nikodým theorems and range theorems to this setting.
An infinite antichain of permutations.