$$\mathrm {ZF}$$ ZF Between Classicality and Non-classicality

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Studia Logica 110 (1):189-218 (2021)
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Abstract

We present a generalization of the algebra-valued models of \ where the axioms of set theory are not necessarily mapped to the top element of an algebra, but may get intermediate values, in a set of designated values. Under this generalization there are many algebras which are neither Boolean, nor Heyting, but that still validate \.

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2022

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10.1007/s11225-021-09959-w

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Giorgio Venturi
University of Campinas

Citations of this work

Ideal Objects for Set Theory.Santiago Jockwich, Sourav Tarafder & Giorgio Venturi - 2022 - Journal of Philosophical Logic 51 (3):583-602.
ZF and its interpretations.S. Jockwich Martinez, S. Tarafder & G. Venturi - 2024 - Annals of Pure and Applied Logic 175 (6):103427.

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References found in this work

Generalized Algebra-Valued Models of Set Theory.Benedikt Löwe & Sourav Tarafder - 2015 - Review of Symbolic Logic 8 (1):192-205.
Non-classical Models of ZF.S. Jockwich Martinez & G. Venturi - 2020 - Studia Logica 109 (3):509-537.
On Negation for Non-classical Set Theories.S. Jockwich Martinez & G. Venturi - 2020 - Journal of Philosophical Logic 50 (3):549-570.

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