Work

The weakness of the Erdős–Moser theorem under arithmetic reductions

Year: 2024

Type: article

Abstract: The Erdős–Moser ([Formula: see text]) theorem says that every infinite tournament admits an infinite transitive subtournament. We study the computational behavior of the [Formula: see text] theorem with respect to the arithmetic hierarchy, and prove that [Formula: see text] instances of [Formula: see text] admit low[Formula: see text] solutions for every [Formula: see text], and that if a set B is not arithmetical, then every instance of [Formula: see text] admits a solution relative to which B is still not arithmetical. We also provide a level-wise refinement of this theorem. These results are part of a larger program of computational study of combinatorial theorems in Reverse Mathematics.

Source: Journal of Mathematical Logic

DOI: 10.1142/s0219061325500011

Authors: Ludovic Levy Patey, Ahmed Mimouni

Institutions: Centre National de la Recherche Scientifique, Université Paris Cité, Institut de Mathématiques de Jussieu-Paris Rive Gauche, Université Paris-Est Créteil, Laboratoire d'Algorithmique, Complexité et Logique

Language: English

Topic: Computability, Logic, AI Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4404414448

FWCI:

Cites: 13

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Related to: 10