Work

Constructive Substitutes for Kőnig’s Lemma

Year: 2025

Type: conference-paper

Abstract: We propose weaker but constructively provable variants of the contrapositive of Kőnig’s lemma. We derive those from a generalization of the FAN theorem for inductive bars to inductive covers, for which we give a concise proof. We compare the positive, negative and sequential characterizations of covers and bars in classical and constructive contexts, giving precise accounts of the role played by the axioms of excluded middle and dependent choice. As an application, we discuss some examples where the use of Kőnig’s lemma can be replaced by one of our weaker variants to obtain fully constructive accounts of results or proofs that could otherwise appear as inherently classical.

Source: HAL (Le Centre pour la Communication Scientifique Directe)

DOI: 10.4230/lipics.types.2024.2

Author: Larchey-Wendling, Dominique

Institutions: Centre National de la Recherche Scientifique, Laboratoire Lorrain de Recherche en Informatique et ses Applications, Université de Lorraine

Language: English

Topic: Computability, Logic, AI Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: Agence Nationale de la Recherche

Award: Non-Aggregative Resource Compositions