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| Full text | |
| Author(s): |
Tarafder, Sourav
Total Authors: 1
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| Document type: | Journal article |
| Source: | JOURNAL OF SYMBOLIC LOGIC; v. 87, n. 1, p. 30-pg., 2021-12-02. |
| Abstract | |
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) | |
| FAPESP's process: | 16/25891-3 - Arbitrariness and genericity: or on how to speak of the unspeakable |
| Grantee: | Giorgio Venturi |
| Support Opportunities: | Research Grants - Young Investigators Grants |