Relational representation for subordination Tarski algebras

ABSTRACT

In this work, we study the relational representation of the class of Tarski algebras endowed with a subordination, called subordination Tarski algebras. These structures were introduced in a previous paper as a generalisation of subordination Boolean algebras. We define the subordination Tarski spaces as topological spaces with a fixed basis endowed with a closed relation. We prove that there exist categorical dualities between categories whose objects are subordination Tarski algebras and categories whose objects are subordination Tarski spaces. These results extend the known dualities for modal algebras. Finally, we are going to characterise some algebraic conditions written in the quasi-modal language by means of first-order conditions.

KEYWORDS:

• Tarski algebras
• subordinations
• quasi-modal operator
• Tarski spaces
• stone spaces

Acknowledgments

We would like to thank the referees for the comments and suggestions on the presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The author acknowledges the partial support of Consejo Nacional de Investigaciones Científicas y Técnicas (PIP 11220200101301CO) and Agencia Nacional de Promoción Científica y Tecnológica (PICT2019-2019-00882, ANPCyT-Argentina), and MOSAIC Project 101007627 (European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie).