Advanced search
Start date
Betweenand
(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

BI-INTERPRETATION IN WEAK SET THEORIES

Full text
Author(s):
Freire, Alfredo Roque [1] ; Hamkins, Joel David [2, 3]
Total Authors: 2
Affiliation:
[1] Univ Brasilia, Philosophy Dept, Brasilia, DF - Brazil
[2] Univ Coll, Philosophy, Oxford - England
[3] Univ Oxford, Log, Fac Philosophy, Dept Math, Oxford - England
Total Affiliations: 3
Document type: Journal article
Source: JOURNAL OF SYMBOLIC LOGIC; v. 86, n. 2, p. 609-634, JUN 2021.
Web of Science Citations: 0
Abstract

In contrast to the robust mutual interpretability phenomenon in set theory, Ali Enayat proved that bi-interpretation is absent: distinct theories extending ZF are never bi-interpretable and models of ZF are bi-interpretable only when they are isomorphic. Nevertheless, for natural weaker set theories, we prove, including Zermelo-Fraenkel set theory ZFC(-) without power set and Zermelo set theory Z, there are nontrivial instances of bi-interpretation. Specifically, there are well-founded models of ZFC- that are bi-interpretable, but not isomorphic-even < H-omega 1, is an element of > and < H-omega 2, is an element of > can be bi-interpretable-and there are distinct bi-interpretable theories extending ZFC-. Similarly, using a construction of Mathias, we prove that every model of ZF is bi-interpretable with a model of Zermelo set theory in which the replacement axiom fails. (AU)

FAPESP's process: 17/21020-0 - On the conditions for a comparison of ontological commitment between theories
Grantee:Alfredo Roque de Oliveira Freire Filho
Support type: Scholarships abroad - Research Internship - Doctorate (Direct)