Affine completeness of de Morgan algebras
Algebraic axiomatization of tense intuitionistic logic
We introduce two unary operators G and H on a relatively pseudocomplemented lattice which form an algebraic axiomatization of the tense quantifiers “it is always going to be the case that” and “it has always been the case that”. Their axiomatization is an extended version for the classical logic and it is in accordance with these operators on many-valued Łukasiewicz logic. Finally, we get a general construction of these tense operators on complete relatively pseudocomplemented lattice which is a...
Algebraic properties of pre-logics
Algebraic theory of stacks
Algebras determined by their endomorphism monoids
Algebras on subintervals of BL-algebras, pseudo BL-algebras and bounded residuated -monoids
Algebras whose principal congruences form a sublattice of the congruence lattice
Algebre di Łukasiewicz quasi-locali Stoneane
We prove some properties of quasi-local Ł-algebras. These properties allow us to give a structure theorem for Stonean quasi-local Ł-algebras. With this characterization we are able to exhibit an example which provides a negative answer to the first problem posed in [4].
Algèbres de Lukasiewicz symétriques
Almost maximal ideals
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 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 application of soft sets to 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 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)).
Annihilator-preserving congruence relations in distributive nearlattices
In this note we give some new characterizations of distributivity of a nearlattice and we study annihilator-preserving congruence relations.
Announcements of new results
Any distributive lattice is determined by a semigroup from a certain class.
Approximate maps, filter monad, and a representation of localic maps
A covariant representation of the category of locales by approximate maps (mimicking a natural representation of continuous maps between spaces in which one approximates points by small open sets) is constructed. It is shown that it can be given a Kleisli shape, as a part of a more general Kleisli representation of meet preserving maps. Also, we present the spectrum adjunction in this approximation setting.