| Full text | |
| Author(s): |
Martinez, S. Jockwich
;
Tarafder, S.
;
Venturi, G.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | ANNALS OF PURE AND APPLIED LOGIC; v. 175, n. 6, p. 38-pg., 2024-03-20. |
| Abstract | |
In this paper, we unify the study of classical and non -classical algebra -valued models of set theory, by studying variations of the interpretation functions for = and is an element of. Although, these variations coincide with the standard interpretation in Boolean -valued constructions, nonetheless they extend the scope of validity of ZF to new algebra -valued models. This paper presents, for the first time, non -trivial paraconsistent models of full ZF. Moreover, due to the validity of Leibniz's law in these structures, we will show how to construct proper models of set theory by quotienting these algebra -valued models with respect to equality, modulo the filter of the designated truth -values. (c) 2024 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/). (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 |
| FAPESP's process: | 19/12527-0 - Algebra-valued models of non-classical set theories |
| Grantee: | Giorgio Venturi |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |
| FAPESP's process: | 17/23853-0 - Arbitrariness and definability in the context of non-classical logics |
| Grantee: | Daniel Santiago Jockwich Martinez |
| Support Opportunities: | Scholarships in Brazil - Doctorate (Direct) |