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An intensional fixed point theory over first order arithmetic

Annals of Pure and Applied Logic 128 (1-3):197-213 (2004)

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Extending constructive operational set theory by impredicative principles.Andrea Cantini - 2011 - Mathematical Logic Quarterly 57 (3):299-322.details We study constructive set theories, which deal with operations applying both to sets and operations themselves. Our starting point is a fully explicit, finitely axiomatized system ESTE of constructive sets and operations, which was shown in 10 to be as strong as PA. In this paper we consider extensions with operations, which internally represent description operators, unbounded set quantifiers and local fixed point operators. We investigate the proof theoretic strength of the resulting systems, which turn out to be impredicative . (...) Download Export citation Bookmark 3 citations
A fixed point theory over stratified truth.Andrea Cantini - 2020 - Mathematical Logic Quarterly 66 (4):380-394.details We present a theory of stratified truth with a μ‐operator, where terms representing fixed points of stratified monotone operations are available. We prove that is relatively intepretable into Quine's (or subsystems thereof). The motivation is to investigate a strong theory of truth, which is consistent by means of stratification, i.e., by adopting an implicit type theoretic discipline, and yet is compatible with self‐reference (to a certain extent). The present version of is an enhancement of the theory presented in [2]. Download Export citation Bookmark

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