Lipschitz and Wadge binary games in second order arithmetic

Andrés Cordón-Franco; F. Félix Lara-Martín; Manuel José Simões Loureiro

Lipschitz and Wadge binary games in second order arithmetic

Andrés Cordón-Franco, F. Félix Lara-Martín, Manuel José Simões Loureiro

EPCV - Escola de Psicologia e Ciências da Vida

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Resumo

We present a detailed formalization of Lipschitz and Wadge games in the context of second order arithmetic and we investigate the logical strength of Lipschitz and Wadge determinacy, and the tightly related Semi-Linear Ordering principle, for the first levels of the Hausdorff difference hierarchy in the Cantor space. As a result, we obtain characterizations of WKL0 and ACA0 in terms of these determinacy principles. Keywords: Reverse mathematics, Determinacy, Wadge games, Semilinear Ordering principle

Idioma original	Inglês
Revista	Default journal
Estado da publicação	Publicadas - 2023

Keywords

MATEMÁTICA
LÓGICA MATEMÁTICA
TEORIA DOS CONJUNTOS

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T1 - Lipschitz and Wadge binary games in second order arithmetic

AU - Cordón-Franco, Andrés

AU - Lara-Martín, F. Félix

AU - Loureiro, Manuel José Simões

N1 - Annals of Pure and Applied Logic

PY - 2023

Y1 - 2023

N2 - We present a detailed formalization of Lipschitz and Wadge games in the context of second order arithmetic and we investigate the logical strength of Lipschitz and Wadge determinacy, and the tightly related Semi-Linear Ordering principle, for the first levels of the Hausdorff difference hierarchy in the Cantor space. As a result, we obtain characterizations of WKL0 and ACA0 in terms of these determinacy principles. Keywords: Reverse mathematics, Determinacy, Wadge games, Semilinear Ordering principle

AB - We present a detailed formalization of Lipschitz and Wadge games in the context of second order arithmetic and we investigate the logical strength of Lipschitz and Wadge determinacy, and the tightly related Semi-Linear Ordering principle, for the first levels of the Hausdorff difference hierarchy in the Cantor space. As a result, we obtain characterizations of WKL0 and ACA0 in terms of these determinacy principles. Keywords: Reverse mathematics, Determinacy, Wadge games, Semilinear Ordering principle

KW - MATEMÁTICA

KW - LÓGICA MATEMÁTICA

KW - TEORIA DOS CONJUNTOS

KW - MATHEMATICS

KW - MATHEMATICAL LOGIC

KW - SET THEORY

UR - http://hdl.handle.net/10437/13951

M3 - Article

SN - 1646-3730

JO - Default journal

JF - Default journal

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