NON-CLASSICAL FOUNDATIONS OF SET THEORY

Autor(es)

Tarafder, Sourav

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF SYMBOLIC LOGIC; v. 87, n. 1, p. 30-pg., 2021-12-02.

Resumo

In this paper, we use algebra-valued models to study cardinal numbers in a class of non-classical set theories. The algebra-valued models of these non-classical set theories validate the Axiom of Choice, if the ground model validates it. Though the models are non-classical, the foundations of cardinal numbers in these models are similar to those in classical set theory. For example, we show that mathematical induction, Cantor's theorem, and the Schroder-Bernstein theorem hold in these models. We also study a few basic properties of cardinal arithmetic. In addition, the generalized continuum hypothesis is proved to be independent of these non-classical set theories. (AU)

• Processo FAPESP: 16/25891-3 - Arbitrariedade e genericidade: ou sobre como falar do indizível
• Beneficiário: Giorgio Venturi
• Modalidade de apoio: Auxílio à Pesquisa - Jovens Pesquisadores