Article
Algebraic combinatorics in bounded induction
Author/s | Borrego Díaz, Joaquín |
Department | Universidad de Sevilla. Departamento de Ciencias de la Computación e Inteligencia Artificial |
Publication Date | 2021 |
Deposit Date | 2021-03-26 |
Published in |
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Abstract | In this paper, new methods for analyzing models of weak subsystems of Peano Arithmetic are proposed. The focus will be on the study of algebro-combinatoric properties of certain definable cuts. Their relationship with ... In this paper, new methods for analyzing models of weak subsystems of Peano Arithmetic are proposed. The focus will be on the study of algebro-combinatoric properties of certain definable cuts. Their relationship with segments that satisfy more induction, with those limited by the standard powers/roots of an element, and also with definable sets in Bounded Induction is studied. As a consequence, some considerations on the Π1-interpretability of IΔ0 in weak theories, as well as some alternative axiomatizations, are reviewed. Some of the results of the paper are obtained by immersing Bounded Induction models in its Stone-Cech Compactification, once it is endowed with a topology. |
Funding agencies | Ministerio de Ciencia, Innovación y Universidades (MICINN). España |
Project ID. | PID2019-109152GB-I00 |
Citation | Borrego Díaz, J. (2021). Algebraic combinatorics in bounded induction. Annals of Pure and Applied Logic, 172 (2) |
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