Título:	An axiomatic approach to forcing and generic extensions
Outros títulos:	Une approche axiomatique du forcing et des extensions génériques
Autor(es):	Freire, Rodrigo de Alvarenga
Assunto:	Axiomas Matemática Lógica
Data de publicação:	2020
Editora:	Centre Mersenne; Académie des sciences, Paris
Referência:	FREIRE, Rodrigo A. An axiomatic approach to forcing and generic extensions. Comptes Rendus Mathématique, v. 358, n. 6, p. 757-775, 2020. DOI: https://doi.org/10.5802/crmath.97. Disponível em: https://comptes-rendus.academie-sciences.fr/mathematique/item/CRMATH_2020__358_6_757_0/. Acesso em: 12 jan. 2020.
Abstract:	This paper provides a conceptual analysis of forcing and generic extensions. Our goal is to give general axioms for the concept of standard forcing-generic extension and to show that the usual (poset) constructions are unified and explained as realizations of this concept. According to our approach, the basic idea behind forcing and generic extensions is that the latter are uniform adjunctions which are groundcontrolled by forcing, and forcing is nothing more than that ground-control. As a result of our axiomatization of this idea, the usual definitions of forcing and genericity are derived.
Résumé:	Cet article présente une analyse conceptuelle du forcing et des extensions génériques. Notre objectif est de donner des axiomes généraux pour le concept d’extension forcing-générique standard, et de montrer que les constructions habituelles sont unifiées et expliquées comme étant des réalisations de ce concept. Selon notre approche, l’idée-clé sous-tendant le forcing et les extensions génériques est que ces dernières sont des adjonctions uniformes qui sont contrôlées par le forcing, ainsi le forcing n’est rien de plus que ce contrôle. Comme conséquence de notre axiomatisation de cette idée, on dérive les définitions habituelles du forcing et de la généricité.
Licença:	© Académie des sciences, Paris and the authors, 2020. Some rights reserved. (CC BY) - This article is licensed under the Creative Commons Attribution 4.0 International License. http://creativecommons.org/licenses/by/4.0/
DOI:	https://doi.org/10.5802/crmath.97
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