The aim of this paper is to give, using the Kripke semantics for intuitionism, a representation of finitely generated free Heyting algebras. By means of the representation we determine in a constructive way some set of "special elements" of such algebras. Furthermore, we show that many algebraic properties which are satisfied by the free algebra on one generator are not satisfied by free algebras on more than one generator.

A new concept of model for the US-tense logic is introduced, in which ternary relations of betweenness are adjoined to the usual early-later relation. The class of these new models, which contains the class of Kripke models, satisfies, contrary to that, the Distinguishable Model Theorem, in the sense that each model is equivalent to a model in which no two points verify exactly the same formulas.

We consider the problem of finding, in the ambit of modal logic, a minimal characterization for finite Kripke frames, i.e., a formula which, given a frame, axiomatizes its theory employing the lowest possible number of variables and implies the other axiomatizations. We show that every finite transitive frame admits a minimal characterization over K4, and that this result can not be extended to K.

We find a short way to construct a formula which axiomatizes a given finite frame of the modal logicK, in the sense that for each finite frameA, we construct a formula A which holds in those and only those frames in which every formula true inA holds.To obtain this result we find, for each finite model and each natural numbern, a formula which holds in those and only those models in which every formula true in , and involving the firstn (...) propositional letters, holds. (shrink)

We define the concepts of minimal p-morphic image and basic p-morphism for transitive Kripke frames. These concepts are used to determine effectively the least number of variables necessary to axiomatize a tabular extension of K4, and to describe the covers and co-covers of such a logic in the lattice of the extensions of K4.

Modal logics with the binary operator Until are considered. It is shown that there exists a continuum of consistent U-logics without Kripke frames, and that each U-logic whose class of order does not have the finite frame property.

The semantics of e-models for tense logics with binary operators for `until' and `since' (US-logics) was introduced by Bellissima and Bucalo in 1995. In this paper we show the adequacy of these semantics by proving a general Henkin-style completeness theorem. Moreover, we show that for these semantics there holds a Stone-like duality theorem with the algebraic structures that naturally arise from US-logics.