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An axiomatic approach to forcing and generic extensions

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 approac...

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Main Author: Freire, Rodrigo de Alvarenga
Format: Artigo
Language: Inglês
Published: Centre Mersenne; Académie des sciences, Paris 2021
Subjects:
Axiomas
Matemática
Lógica
Online Access: https://repositorio.unb.br/handle/10482/39890
https://doi.org/10.5802/crmath.97
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spelling ir-10482-398902021-01-22T15:06:11Z An axiomatic approach to forcing and generic extensions Une approche axiomatique du forcing et des extensions génériques Freire, Rodrigo de Alvarenga Axiomas Matemática Lógica 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. 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. 2021-01-12T19:02:44Z 2021-01-12T19:02:44Z 2020 Artigo 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. https://repositorio.unb.br/handle/10482/39890 https://doi.org/10.5802/crmath.97 Inglês Acesso Aberto © 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/ application/pdf Centre Mersenne; Académie des sciences, Paris
institution REPOSITORIO UNB
collection REPOSITORIO UNB
language Inglês
topic Axiomas
Matemática
Lógica
spellingShingle Axiomas
Matemática
Lógica
Freire, Rodrigo de Alvarenga
An axiomatic approach to forcing and generic extensions
description 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.
format Artigo
author Freire, Rodrigo de Alvarenga
author_sort Freire, Rodrigo de Alvarenga
title An axiomatic approach to forcing and generic extensions
title_short An axiomatic approach to forcing and generic extensions
title_full An axiomatic approach to forcing and generic extensions
title_fullStr An axiomatic approach to forcing and generic extensions
title_full_unstemmed An axiomatic approach to forcing and generic extensions
title_sort axiomatic approach to forcing and generic extensions
publisher Centre Mersenne; Académie des sciences, Paris
publishDate 2021
url https://repositorio.unb.br/handle/10482/39890
https://doi.org/10.5802/crmath.97
_version_ 1690679526542016512
score 13.657419

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