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arXiv · 1810.07437

Disjunctions with stopping condition

Roman Kossak·Bartosz Wcisło
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Abstract

We introduce a tool for analysing models of $\textnormal{CT}^-$, the compositional truth theory over Peano Arithmetic. We present a new proof of Lachlan's theorem that arithmetical part of models of $\textnormal{PA}$ are recursively saturated. We use this tool to provide a new proof that all models of $\textnormal{CT}^-$ carry a partial inductive truth predicate. Finally, we construct a partial truth predicate defined for formulae from a nonstandard cut which cannot be extended to a full truth predicate satisfying $\textnormal{CT}^-$.

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Roman Kossak, Bartosz Wcisło. 2018-10-17. Disjunctions with stopping condition. https://arxiv.org/abs/1810.07437

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