English

Disjunctions with stopping condition

Logic 2020-10-16 v2

Abstract

We introduce a tool for analysing models of CT\textnormal{CT}^-, the compositional truth theory over Peano Arithmetic. We present a new proof of Lachlan's theorem that arithmetical part of models of PA\textnormal{PA} are recursively saturated. We use this tool to provide a new proof that all models of CT\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 CT\textnormal{CT}^-.

Keywords

Cite

@article{arxiv.1810.07437,
  title  = {Disjunctions with stopping condition},
  author = {Roman Kossak and Bartosz Wcisło},
  journal= {arXiv preprint arXiv:1810.07437},
  year   = {2020}
}

Comments

22 pages

R2 v1 2026-06-23T04:42:52.318Z