Santiago Jockwich

• Jockwich, Daniel Santiago (2025). A Model of Connexive Set Theory. Studia Logica: An International Journal for Symbolic Logic. ISSN 0039-3215. doi: 10.1007/s11225-025-10180-2. Full text in Research Archive Show summary

  In this paper, we explore the possibility of constructing algebra-valued models for connexive set theories. In particular, we build an algebra-valued model on top of the four-element lattice MC which semantically captures Wansing’s logic of material connexvity (MC). We show that the resulting model validates an axiom system that is classically equivalent to ZF and that its underlying logic is a connexive logic. For this purpose, we tweak our semantic interpretation of set-membership and identity resulting in a model with a classical notion of identity and a non-classical notion of set-membership. Finally, in the conclusion, we discuss the role of our model within the ongoing debate between logical pluralism and monism.

• Jockwich, Daniel Santiago (2025). Logical Pluralism via Mathematical Convergence. Erkenntnis: An International Journal of Scientific Philosophy. ISSN 0165-0106. doi: 10.1007/s10670-025-00954-4. Full text in Research Archive Show summary

  We propose a novel approach to logical pluralism based on algebra-valued models of set theory, systematically demonstrating how both classical and non-classical set theories can be constructed within a unified mathematical framework. Our approach extends Shapiro’s eclectic pluralism to the specific setting of algebra-valued models. This leads us to formulate two notions of logical pluralism: liberal pluralism, which recognizes as legitimate any logic that underpins a set theory capable of capturing a significant portion of mathematical practice, and strict pluralism, which further requires that the resulting set theory satisfies a convergence constraint, ensuring its mathematical expressiveness is comparable to that of classical set theory. We argue that this latter notion of pluralism represents a departure from previous accounts, as it is based on convergence rather than divergence among classical and non-classical mathematical theories.

• Jockwich, Daniel Santiago; Venturi, Giorgio & Tarafder, Sourav (2024). ZF and its interpretations. Annals of Pure and Applied Logic. ISSN 0168-0072. 175(6). doi: 10.1016/j.apal.2024.103427. Full text in Research Archive Show summary

  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 ∈. 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.

• Gruszczyński, Rafał & Jockwich, Daniel Santiago (2024). Grzegorczyk and Whitehead Points: The Story Continues. Journal of Philosophical Logic. ISSN 0022-3611. doi: 10.1007/s10992-024-09747-6. Full text in Research Archive Show summary

  The paper is devoted to the analysis of two seminal definitions of points within the region-based framework: one by Whitehead (1929) and the other by Grzegorczyk (Synthese, 12(2-3), 228-235 1960). Relying on the work of Biacino & Gerla (Notre Dame Journal of Formal Logic, 37(3), 431-439 1996), we improve their results, solve some open problems concerning the mutual relationship between Whitehead and Grzegorczyk points, and put forward open problems for future investigation.

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