A Lindstr\"om theorem for intuitionistic propositional logic

TL;DR

This paper establishes a Lindström-type theorem characterizing propositional intuitionistic logic as the most expressive logic satisfying specific topological and invariance properties.

Contribution

It introduces a Lindström theorem for intuitionistic propositional logic, identifying it as the maximal logic with certain topological and invariance features.

Findings

Propositional intuitionistic logic is maximal under specified properties.

The logic satisfies a topological property similar to compactness.

It is preserved under asimulations.

Abstract

It is shown that propositional intuitionistic logic is the maximal (with respect to expressive power) abstract logic satisfying a certain topological property reminiscent of compactness, the Tarski union property and preservation under asimulations.