Generalizations of the Weak Law of the Excluded Middle

TL;DR

This paper explores a broad class of formulas extending the weak law of the excluded middle, characterizing them through Kripke frames and Brouwer algebras, and applying these to distinguish logics in the Medvedev lattice.

Contribution

It introduces a generalization of the weak law of the excluded middle and characterizes these formulas via Kripke frames and Brouwer algebras, enabling separation of logics in the Medvedev lattice.

Findings

Characterization of generalized formulas using Kripke frames

Representation of formulas in Brouwer algebras

Separation of logics in the Medvedev lattice

Abstract

We study a class of formulas generalizing the weak law of the excluded middle, and provide a characterization of these formulas in terms of Kripke frames and Brouwer algebras. We use these formulas to separate logics corresponding to factors of the Medvedev lattice.