Models of PT- with Internal Induction for Total Formulae

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Review of Symbolic Logic 10 (1):187-202 (2017)
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Abstract

We show that a typed compositional theory of positive truth with internal induction for total formulae (denoted by PT tot ) is not semantically conservative over Peano arithmetic. In addition, we observe that the class of models of PA expandable to models of PT tot contains every recursively saturated model of arithmetic. Our results point to a gap in the philosophical project of describing the use of the truth predicate in model-theoretic contexts.

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10.1017/s1755020316000356

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Citations of this work

Disjunctions with stopping conditions.Roman Kossak & Bartosz Wcisło - 2021 - Bulletin of Symbolic Logic 27 (3):231-253.
Models of positive truth.Mateusz Łełyk & Bartosz Wcisło - 2019 - Review of Symbolic Logic 12 (1):144-172.

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References found in this work

Proof and Truth.Stewart Shapiro - 1998 - Journal of Philosophy 95 (10):493-521.
Notes on Formal Theories of Truth.Andrea Cantini - 1989 - Mathematical Logic Quarterly 35 (2):97-130.
Notes on Formal Theories of Truth.Andrea Cantini - 1989 - Zeitshrift für Mathematische Logik Und Grundlagen der Mathematik 35 (1):97--130.
Relative truth definability of axiomatic truth theories.Kentaro Fujimoto - 2010 - Bulletin of Symbolic Logic 16 (3):305-344.

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