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  1.  42
    Generalized Algebra-Valued Models of Set Theory.Benedikt Löwe & Sourav Tarafder - 2015 - Review of Symbolic Logic 8 (1):192-205.
  2.  11
    Independence Proofs in Non-Classical Set Theories.Sourav Tarafder & Giorgio Venturi - forthcoming - Review of Symbolic Logic:1-32.
  3.  7
    $$\mathrm {ZF}$$ ZF Between Classicality and Non-classicality.Sourav Tarafder & Giorgio Venturi - 2022 - Studia Logica 110 (1):189-218.
    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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  4.  1
    Non-Classical Foundations of Set Theory.Sourav Tarafder - 2022 - Journal of Symbolic Logic 87 (1):347-376.
    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 Schröder–Bernstein theorem hold in these models. We also study a few basic (...)
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  5.  11
    Ideal Objects for Set Theory.Santiago Jockwich, Sourav Tarafder & Giorgio Venturi - forthcoming - Journal of Philosophical Logic:1-20.
    In this paper, we argue for an instrumental form of existence, inspired by Hilbert’s method of ideal elements. As a case study, we consider the existence of contradictory objects in models of non-classical set theories. Based on this discussion, we argue for a very liberal notion of existence in mathematics.
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