arXiv subjects

Katarzyna Słomczyńska

Publications and source records attributed to Katarzyna Słomczyńska.

6 recordsLinked to original sources

arXiv2026

A generic construction of free algebras in varieties of Hilbert algebras and Brouwerian semilattices

We give a generic construction of the n-generated free Hilbert algebras and Brouwerian semilattices by a uniform method applicable to any variety of Hilbert algebras or Brouwerian semilattices, as long as a manageable description of subdirectly irreducible algebras in that variety is available. A slight modification yields analogous constructions for varieties of Hilbert algebras and Brouwerian semilattices with zero. As examples we construct free algebras in varieties of bounded height and of bounded width; we also find a closed formula for the free spectrum of linear Hilbert algebras. Finally, we obtain a few results on structural completeness of varieties of Hilbert algebras with zero, in particular, we give a sufficient condition for a quasi-equation to be equivalent to an equation.

math.LO↗

arXiv2024

Quasivarieties of p-algebras: some new results

We investigate quasivarieties of (distributive) p-algebras. We sharpen some previous results, give a better picture of the subquasivariety lattice, and prove that quasivarieties generated by free p-algebras belong to a rather small quasivariety characterised by excluding all but 3 subdirectly irreducibles.

math.LO↗

arXiv2024

Decidable varieties of p-algebras

We show that for quasivarieties of p-algebras the properties of (i) having decidable first-order theory and (ii) having decidable first-order theory of the finite members, coincide. The only two quasivarieties with these properties are the trivial variety and the variety of Boolean algebras. This contrasts sharply, even for varieties, with the situation in Heyting algebras where decidable varieties do not coincide with finitely decidable ones.

math.LO↗

arXiv2024

Free p-algebras revisited: an algebraic investigation of implication-free intuitionism

We give a new construction of free distributive p-algebras. Our construction relies on a detailed description of completely meet-irreducible congruences, so it is purely universal algebraic. It yields a normal form theorem for p-algebra terms, simpler proofs of several existing results, as well as a complete characterisation of structurally complete varieties of p-algebras.

math.LO↗

arXiv2021

The structure of completely meet irreducible congruences in strongly Fregean algebras

A strongly Fregean algebra is an algebra such that the class of its homomorphic images is Fregean and the variety generated by this algebra is congruence modular. To understand the structure of these algebras we study the prime intervals projectivity relation in the posets of their completely meet irreducible congruences and show that its cosets have natural structure of Boolean group. In particular, this approach allows us to represent congruences and elements of such algebras as the subsets of upward closed subsets of these posets with some special properties.

math.RA↗

arXiv2010

Unification and projectivity in Fregean varieties

In some varieties of algebras one can reduce the question of finding most general unifiers (mgus) to the problem of the existence of unifiers that fulfill the additional condition called projectivity. In this paper we study this problem for Fregean (1-regular and orderable) varieties that arise from the algebraization of fragments of intuitionistic or intermediate logics. We investigate properties of Fregean varieties, guaranteeing either for a given unifiable term or for all unifiable terms, that projective unifiers exist. We indicate the identities which fully characterize congruence permutable Fregean varieties having projective unifiers. In particular, we show that for such a variety there exists the largest subvariety that have projective unifiers.

math.LO↗