Subordination Tarski algebras. Issue 3 (3rd July 2019)

• Record Type: Journal Article
• Authors: Celani, Sergio A.
• Is Part Of: Journal of applied non-classical logics. Volume 29:Issue 3(2019)
• Page Start: 288
• Page End: 306
• Publication Date: 2019-07-03
• Subjects: Tarski algebras -- subordinations -- quasi-modal operator -- round filters -- topological and monadic algebras; Nonclassical mathematical logic -- Periodicals; Wiskundige logica; Logic; Periodicals; 511.3105
• DOI: 10.1080/11663081.2019.1638080
• Languages: English
• ISSNs: 1166-3081

Abstract

ABSTRACT: In this work we will study Tarski algebras endowed with a subordination, called subordination Tarski algebras. We will define the notion of round filters, and we will study the class of irreducible round filters and the maximal round filters, called ends. We will prove that the poset of all round filters is a lattice isomorphic to the lattice of the congruences that are compatible with the subordination. We will prove that every end is an irreducible round filter, and that in a topological subordination Tarski algebra A, every irreducible round filter is an end iff A is a monadic subordination Tarski algebra. As corollary of this result we have that the variety of monadic Tarski algebra can be characterised as the topological Tarski algebras where every irreducible open filter is a maximal open filter.