Some notes on the superintuitionistic logic of chequered subsets of $\mathbb{R}^\infty$

TL;DR

This paper explores the superintuitionistic logic related to chequered subsets of infinite-dimensional real space, revealing its properties and its relation to known modal and Medvedev logics.

Contribution

It characterizes the superintuitionistic analogue of the chequered subset modal logic, identifying key axioms and logical properties, and situates it within the landscape of existing logics.

Findings

The logic has the disjunction property.

It contains the Scott axiom.

It does not contain the Kreisel-Putnam axiom.

Abstract

I investigate the superintuitionistic analogue of the modal logic of chequered subsets of $\mathbb{R}^\infty$ introduced by van Benthem et al. It is observed that this logic possesses the disjunction property, contains the Scott axiom, fails to contain the Kreisel-Putnam axiom and it is a sublogic of the Medvedev logic.