A note on the fixed point for the polynomials of a boolean algebra with an operator of endomorphism
A survey on lifting in measure theory
Algebraic representation of continua.
Boolean differential operators
We consider four combinatorial interpretations for the algebra of Boolean differential operators and construct, for each interpretation, a matrix representation for the algebra of Boolean differential operators.
Complete description for -equivalence types of superatomic -algebras.
Discriminator varieties of Boolean algebras with residuated operators
The theory of discriminator algebras and varieties has been investigated extensively, and provides us with a wealth of information and techniques applicable to specific examples of such algebras and varieties. Here we give several such examples for Boolean algebras with a residuated binary operator, abbreviated as r-algebras. More specifically, we show that all finite r-algebras, all integral r-algebras, all unital r-algebras with finitely many elements below the unit, and all commutative residuated...
Generalized join-hemimorphisms on Boolean algebras.
Many-sorted coalgebraic modal logic : a model-theoretic study
This paper gives a semantical underpinning for a many-sorted modal logic associated with certain dynamical systems, like transition systems, automata or classes in object-oriented languages. These systems will be described as coalgebras of so-called polynomial functors, built up from constants and identities, using products, coproducts and powersets. The semantical account involves Boolean algebras with operators indexed by polynomial functors, called MBAOs, for Many-sorted Boolean Algebras with...
Many-Sorted Coalgebraic Modal Logic: a Model-theoretic Study
This paper gives a semantical underpinning for a many-sorted modal logic associated with certain dynamical systems, like transition systems, automata or classes in object-oriented languages. These systems will be described as coalgebras of so-called polynomial functors, built up from constants and identities, using products, coproducts and powersets. The semantical account involves Boolean algebras with operators indexed by polynomial functors, called MBAOs, for Many-sorted Boolean Algebras with...
Marczewski-Burstin Representations of Boolean Algebras Isomorphic to a Power Set
The paper contains some sufficient conditions for Marczewski-Burstin representability of an algebra 𝓐 of sets which is isomorphic to 𝓟(X) for some X. We characterize those algebras of sets which are inner MB-representable and isomorphic to a power set. We consider connections between inner MB-representability and hull property of an algebra isomorphic to 𝓟 (X) and completeness of an associated quotient algebra. An example of an infinite universally MB-representable algebra is given.
On BPI Restricted to Boolean Algebras of Size Continuum
(i) The statement P(ω) = “every partition of ℝ has size ≤ |ℝ|” is equivalent to the proposition R(ω) = “for every subspace Y of the Tychonoff product the restriction |Y = Y ∩ B: B ∈ of the standard clopen base of to Y has size ≤ |(ω)|”. (ii) In ZF, P(ω) does not imply “every partition of (ω) has a choice set”. (iii) Under P(ω) the following two statements are equivalent: (a) For every Boolean algebra of size ≤ |ℝ| every filter can be extended to an ultrafilter. (b) Every Boolean algebra of...
Quasi-modal algebras
In this paper we introduce the class of Boolean algebras with an operator between the algebra and the set of ideals of the algebra. This is a generalization of the Boolean algebras with operators. We prove that there exists a duality between these algebras and the Boolean spaces with a certain relation. We also give some applications of this duality.
Regulated semilattices and locally compact spaces
Subalgebras of diagonalizable algebras of theories containing arithmetic [Book]
Subdirectly irreducible quasi-modal 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...
Автоустойчивость булевых алгебр с выделенным идеалом.
Базисы допустимых правил вывода табличных модальных логик глубины 2.
Изоморфные подалгебры вероятностных булевых алгебр