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  1. Bounded finite set theory.Laurence Kirby - 2021 - Mathematical Logic Quarterly 67 (2):149-163.
    We define an axiom schema for finite set theory with bounded induction on sets, analogous to the theory of bounded arithmetic,, and use some of its basic model theory to establish some independence results for various axioms of set theory over. Then we ask: given a model M of, is there a model of whose ordinal arithmetic is isomorphic to M? We show that the answer is yes if.
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  • Constructive Ackermann's interpretation.Hanul Jeon - 2022 - Annals of Pure and Applied Logic 173 (5):103086.
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  • A theory of implicit commitment.Mateusz Łełyk & Carlo Nicolai - 2022 - Synthese 200 (4):1-26.
    The notion of implicit commitment has played a prominent role in recent works in logic and philosophy of mathematics. Although implicit commitment is often associated with highly technical studies, it remains an elusive notion. In particular, it is often claimed that the acceptance of a mathematical theory implicitly commits one to the acceptance of a Uniform Reflection Principle for it. However, philosophers agree that a satisfactory analysis of the transition from a theory to its reflection principle is still lacking. We (...)
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