Subdirectly irreducible algebras of quasiordered logics
Subdirectly irreducible quasi-modal algebras.
Subspaces in abstract Stone duality.
Super-De Morgan functions and free De Morgan quasilattices
A De Morgan quasilattice is an algebra satisfying hyperidentities of the variety of De Morgan algebras (lattices). In this paper we give a functional representation of the free n-generated De Morgan quasilattice with two binary and one unary operations. Namely, we define the concept of super-De Morgan function and prove that the free De Morgan quasilattice with two binary and one unary operations on nfree generators is isomorphic to the De Morgan quasilattice of super-De Morgan functions of nvariables....
Sur les algèbres de Heyting symétriques
Symmetrische Zerlegung von Kettenprodukten.
Systems of equations over finite Boolean algebras
Systems Of Linear Boolean Equations
Systems of linear Boolean equations.
Teorema de Ramsey aplicado a álgebras de Boole.
Some properties of Boolean algebras are characterized through the topological properties of a certain space of countable sequences of ordinals. For this, it is necessary to prove the Ramsey theorems for an arbitrary infinite cardinal. Also, we define continuous mappings on these spaces from vector measures on the algebra.
The 0-distributivity in the class of subalgebra lattices of Heyting algebras and closure algebras
The class of 2-dimensional neat reducts is not elementary
SC, CA, QA and QEA stand for the classes of Pinter's substitution algebras, Tarski's cylindric algebras, Halmos' quasipolyadic algebras and Halmos' quasipolyadic algebras with equality, respectively. Generalizing a result of Andréka and Németi on cylindric algebras, we show that for K ∈ SC,QA,CA,QEA and any β > 2 the class of 2-dimensional neat reducts of β-dimensional algebras in K is not closed under forming elementary subalgebras, hence is not elementary. Whether this result extends to higher...
The combinatorial derivation and its inverse mapping
Let G be a group and P G be the Boolean algebra of all subsets of G. A mapping Δ: P G → P G defined by Δ(A) = {g ∈ G: gA ∩ A is infinite} is called the combinatorial derivation. The mapping Δ can be considered as an analogue of the topological derivation d: P X→ P X, A ↦ A d, where X is a topological space and A d is the set of all limit points of A. We study the behaviour of subsets of G under action of Δ and its inverse mapping ∇. For example, we show that if G is infinite and I is an ideal in...
The Countable Chain Condition and Free Algebras.
The dependence of some logical axioms on disjoint transversals and linked systems
The distributivity numbers of finite products of P(ω)/fin
Generalizing [ShSp], for every n < ω we construct a ZFC-model where ℌ(n), the distributivity number of r.o., is greater than ℌ(n+1). This answers an old problem of Balcar, Pelant and Simon (see [BaPeSi]). We also show that both Laver and Miller forcings collapse the continuum to ℌ(n) for every n < ω, hence by the first result, consistently they collapse it below ℌ(n).
The elementary-equivalence classes of clopen algebras of P-spaces
Two Boolean algebras are elementarily equivalent if and only if they satisfy the same first-order statements in the language of Boolean algebras. We prove that every Boolean algebra is elementarily equivalent to the algebra of clopen subsets of a normal P-space.
The equivalence of Boolean prime ideal theorem and a theorem of functional analysis
The Formulas of the General Reproductive Solution of an Equation in Boolean Ring with Unit
The lattice of subvarieties of the biregularization of the variety of Boolean algebras
Let τ: F → N be a type of algebras, where F is a set of fundamental operation symbols and N is the set of all positive integers. An identity φ ≈ ψ is called biregular if it has the same variables in each of it sides and it has the same fundamental operation symbols in each of it sides. For a variety V of type τ we denote by the biregularization of V, i.e. the variety of type τ defined by all biregular identities from Id(V). Let B be the variety of Boolean algebras of type , where and . In...