# About a 'concrete' Rauszer Boolean algebra generated by a preorder

## TL;DR

This paper explores a specific 'concrete' Rauszer Boolean algebra generated by a preorder, providing a framework for representing various algebraic structures related to logic.

## Contribution

It introduces a general framework for representing algebraic structures associated with logic using a concrete Rauszer Boolean algebra derived from a preorder.

## Key findings

- Provides a representation framework for algebraic structures in logic.
- Connects Rauszer Boolean algebras with Heyting-Brouwer subalgebras.
- Extends previous results by Halmos, Monteiro, and Rauszer.

## Abstract

Inspired by the fundamental results obtained by P. Halmos and A. Monteiro, concerning equivalence relations and monadic Boolean algebras, we recall the `concrete' Rauszer Boolean algebra pointed out by C. Rauszer (1971), via un preorder R. On this algebra we can consider one of the several binary operations defined, in an abstract way, by A. Monteiro (1971). The Heyting-Brouwer subalgebra of constants (fixpoints), allows us to give a general framework to find representations of several special algebraic structures related to logic.