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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 va
Externí odkaz:
http://arxiv.org/abs/2409.09015
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 chara
Externí odkaz:
http://arxiv.org/abs/2409.08990
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, simple
Externí odkaz:
http://arxiv.org/abs/2405.14581
On an arbitrary meet-semilattice S with 0 we define an orthogonality relation and investigate the lattice Cl(S) of all subsets of S closed under this orthogonality. We show that if S is atomic then Cl(S) is a complete atomic Boolean algebra. If S is
Externí odkaz:
http://arxiv.org/abs/2404.13361
Autor:
Chajda, Ivan, Länger, Helmut
Two kinds of the connective implication are introduced as term operations of a pseudocomplemented lattice. It is shown that they share a lot of properties with the intuitionistic implication based on Heyting algebras. In particular, if the pseudocomp
Externí odkaz:
http://arxiv.org/abs/2401.05541
Autor:
Chajda, Ivan, Länger, Helmut
Investigating the structure of pseudocomplemented lattices started ninety years ago with papers by V. Glivenko, G. Birkhoff and O. Frink and this structure was essentially developed by G. Gr\"atzer. In recent years, some special filters in pseudocomp
Externí odkaz:
http://arxiv.org/abs/2312.04685
Autor:
Chajda, Ivan, Länger, Helmut
The aim of the present paper is to show that the concept of intuitionistic logic based on a Heyting algebra can be generalized in such a way that it is formalized by means of a bounded poset. In this case it is not assumed that the poset is relativel
Externí odkaz:
http://arxiv.org/abs/2308.11350
M.S. Rao recently investigated some sorts of special filters in distributive pseudocomplemented lattices. In our paper we extend this study to lattices which need neither be distributive nor pseudocomplemented. For this sake we define a certain modif
Externí odkaz:
http://arxiv.org/abs/2306.09958
Autor:
He, Peng, Wang, Xue-ping
In this article, we first characterize pseudocomplemented inductive modular lattices by using their two 0-sublattices. Then we use two 0-sublattices of a subgroup lattice to describe all locally cyclic abelian groups. In particular, we show that a lo
Externí odkaz:
http://arxiv.org/abs/2211.01337
Publikováno v:
Math. Slovaca 73 (2023), 1-16
In 1973, Katri\v{n}\'{a}k proved that regular double $p$-algebras can be regarded as (regular) double Heyting algebras by ingeniously constructing binary terms for the Heying implication and its dual in terms of pseudocomplement and its dual. In this
Externí odkaz:
http://arxiv.org/abs/2210.10387