Disjunctions with stopping condition
Abstract
We introduce a tool for analysing models of CT-, the compositional truth theory over Peano Arithmetic. We present a new proof of Lachlan's theorem that arithmetical part of models of PA are recursively saturated. We use this tool to provide a new proof that all models of 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 CT-.
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