Logics of formal inconsistency and mathematical definability

Abstract This paper revisits the model theory of logics of formal inconsistency. I investigate how adopting the minimal system QmbC as a foundational framework affects the standard logical conditions of mathematical definability. In a classical setting, mathematical definability is tied to the validity of the Fraïssé definability property. This property states that a concept is first-order definable if, and only if, its satisfiability is preserved under partial isomorphism. In QmbC, Fraïssé definability property fails. Instead, we only recover a weaker version of this theorem. To demonstrate this, I elaborate on preliminary results from Mendonça and Carnielli (2020, Logic J. IGPL, 28, 10601072) and Mendonça (Traditional Theory of Semantic Information without Scandal of Deduction: A Moderately Externalist Reassessment of the Topic Based on Urn Semantics and a Paraconsistent Application. PhD Thesis. Unicamp, Brazil, 2018) . The present findings indicate that, in a paraconsistent context, the universe of mathematically definable notions is significantly restricted.