Disjunctions with stopping condition
Roman Kossak, Bartosz Wcisło · arXiv (Cornell University) · 2018
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 $\textnormal{CT}^-$.