
Authors:
Teresa BIEGANSKA and Katarzyna HALKOWSKA
Title:Generics of Pcompatible Varieties
Pages:17
File:bibtex
Abstract ( + )
or every variety V there exists an algebra A generating V by means of direct products, subalgebras and homomorphic images, i.e. V=HSP(A). Such algebras are called generics of V. Obviously, the free algebra over V with ω generators is a generic of V. The aim of this paper is to find finite generics for some Pcompatible varieties.

Authors:
Luis F. CACERESDUQUE
Title:Ideal Theories of some Commutative Rings
Pages:918
File:bibtex
Abstract ( + )
Associated with the congruence relations of any algebra U there is a propositional theory T(U) whose models are exactly the congruences of U. In particular, given a commutative ring R with 1 it is possible to show that for any consistent extension T of T(R) there must always be a sentence α such that (T u {α}) has a unique model, called an atomic ideal of T. We define extensions of T(R) which are analogous to taking the CantorBendixon derivative in a topological space and we present some particular examples of atomic ideals of these theories in some commutative rings.

Authors:
Wojciech DZIK
Title:Unitary Unification of S5 Modal Logic and its Extensions
Pages:1926
File:bibtex
Abstract ( + )
It is shown that all extensions of S5 modal logic, both in the standard formalization and in the formalization with strict implication, as well as all varieties of monadic algebras have unitary unification.

Authors:
Joanna GRYGIEL
Title:On Gluing of Lattices
Pages:2732
File:bibtex
Abstract ( + )
We compare the operation on lattices given by A. Wronski to the operation of gluing of bounded lattices according to a skeleton introduced by Ch. Herrmann. We prove that these operations differ in many respects. In particular, sumirreducible lattices with respect to these operations do not coincide.

Authors:
Jadwiga KNOP
Title:About a Certain Generalization of the Affine Ratio of Three Points and Unharmonic Ratio of Four Points
Pages:3342
File:bibtex
Abstract ( + )
The paper refers to a certain generalization of the affine ratio. As it is known the affine ratio is defined for three collinear points. The paper gives a definition of the ndimensional affine ratio for n+2 points belonging to an ndimensional affine subspace. If n=1, then we obtain a definition of the affine ratio of three points. We also define the twodimensional unharmonic ratio of five projective points. For proper points the twodimensional unharmonic ratio can be expressed in terms of the twodimensional affine ratio.

Authors:
Zofia KOSTRZYCKA and Marek ZAIONC
Title:On the Density of Truth in Dummett's Logic
Pages:4355
File:bibtex
Abstract ( + )
For the given logical calculus we investigate the size of the fraction of true formulas of a certain length n against the number of all formulas of this length. We are especially interested in asymptotic behaviour of this fraction when n tends to infinity. If the limit of the fraction exists it represents a number which we call the density of truth for the investigated logic. In this paper we apply this approach to the Dummett intermediate linear logic. This paper shows the exact density of this logic and demonstrates that it covers a substantial part of classical propositional calculus. In fact, despite strictly mathematical means used to solve all discussed problems, this paper may have a philosophical impact on understanding to what extent the phenomenon of truth is sporadic or frequent in random mathematics sentences.

Authors:
Krystyna MRUCZEKNASIENIEWSKA
Title:Subdirectly Irreducible Pcompatible Abelian Groups
Pages:5763
File:bibtex
Abstract ( + )
Identities of some special structure like regular identities, normal identities, externally compatible identities and generalization of the last two: Pcompatible identities have been studied since the sixties. They have been determined by the structure of terms occurring in them.
In this paper we describe all subdirectly irreducible algebras from the variety defined by all Pcompatible identities of the Abelian groups.

Authors:
Tomasz POLACIK
Title:Quantified Intuitionistic Propositional Logic and Cantor Space
Pages:6574
File:bibtex
Abstract ( + )
We consider propositional quantification in intuitionistic logic. We prove that, under topological interpretation over Cantor space, it enjoys surprising and interesting properties such as maximum property and a kind of distribution of existential quantifier over conjunction. Moreover, by pointing to the appropriate examples, we show that the set of quantified formulas valid in Cantor space strictly contains the set of formulas provable in the minimal system of intuitionistic logic with propositional quantification.

Authors:
Bozena STARUCH
Title:Derivation from Partial Knowledge in Partial Models
Pages:7584
File:bibtex
Abstract ( + )
We consider partial model, i.e. extensions of partial algebras by predicates, and we define for them the operator of possibility on sets of first order sentences.

Authors:
Bozena STARUCH and Bogdan STARUCH
Title:Possible Sets of Equations
Pages:8595
File:bibtex
Abstract ( + )
We investigate equations for a given partial algebra by appealing to the class of all total algebras it makes part of.