The smallest and largest elements of L are denoted 0 and 1 respectively, so PL(0) is the empty set and PL(1) is the spectrum of L. As a ranges over L, PL(a) form a basis of closed sets for the so-called Zariski’s topology on Spec(L) which turns Spec(L) into a spectral space, that is a topological space homeomorphic to the spectrum of a ring. The following definitions for an element a and a prim...

assume that $a$‎, ‎$b$ are banach algebras and that $m:atimes brightarrow b$‎, ‎$m^prime:atimes arightarrow b$ are bounded bilinear mappings‎. ‎we study the relationships between arens regularity of $m$‎, ‎$m^prime$ and the banach algebras $a$‎, ‎$b$‎. ‎for a banach $a‎$‎-bimodule $b$‎, ‎we show that $b$ factors with respect to $a$ if and only if $b^{**}$ is unital as an $a^{**}‎$‎-module‎. ‎le...

This paper presents a simple decision method for positively quantified formulae of the classical firstorder theory LOHA of linearly ordered Heyting algebras, where by positively quantified we mean that universal quantifiers appear only in positive positions and existential quantifiers appear only in negative positions. Π1-formulae are examples. In particular, word problems, either in LOHA or in...

Ordered algebras such as Boolean algebras, Heyting algebras, lattice-ordered groups, and MV-algebras have long played a decisive role in logic, although perhaps only in recent years has the significance of the relationship between the two fields begun to be fully recognized and exploited. The first aim of this survey article is to briefly trace the distinct historical roots of ordered algebras ...

The lter construction, as an endo-functor on the category of small coherent categories, was used extensively by A. Pitts in a series of papers in the 80's to prove completeness and interpolation results. Later I. Moerdijk and E. Palmgren used the lter construction to construct non-standard models of Heyting arithmetic. In this paper we describe lter construction as a left-adjoint: applied to a ...

In this paper we study frame definability in finitely valued modal logics and establish two main results via suitable translations: (1) one cannot define more classes of frames than are already definable classical logic (cf. [27, Thm. 8]), (2) a large family exactly the same as (including based on finite Heyting MV-algebras, or even BL-algebras). way may observe, for example, that celebrated Go...

A commutative residuated lattice is said to be subidempotent if the lower bounds of its neutral element e are idempotent (in which case they naturally constitute a Brouwerian algebra A*). It proved here that epimorphisms surjective in variety K such algebras (with or without involution), provided each finitely subdirectly irreducible B has two properties: (1) generated by e, and (2) poset prime...

The variety QH of Heyting algebras with a quantifier [14] corresponds to the algebraic study of the modal intuitionistic propositional calculus without the necessity operator. This paper is concerned with the subvariety C of QH generated by chains. We prove that this subvariety is characterized within QH by the equations ∇(x∧ y) ≈ ∇x∧∇y and (x → y)∨ (y → x) ≈ 1. We investigate free objects in C.

Abstract. The present paper contributes to the development of the mathematical theory of epistemic updates using the tools of duality theory. Here we focus on Probabilistic Dynamic Epistemic Logic (PDEL). We dually characterize the product update construction of PDEL-models as a certain construction transforming the complex algebras associated with the given model into the complex algebra assoc...