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DISJUNCTIONS WITH STOPPING CONDITIONS
- Part of
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- Journal:
- Bulletin of Symbolic Logic / Volume 27 / Issue 3 / September 2021
- Published online by Cambridge University Press:
- 05 January 2021, pp. 231-253
- Print publication:
- September 2021
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- Article
- Export citation
-
We introduce a tool for analysing models of
$\text {CT}^-$
, the compositional truth theory over Peano Arithmetic. We present a new proof of Lachlan’s theorem that the arithmetical part of models of 
$\text {CT}^-$
are recursively saturated. We also use this tool to provide a new proof of theorem from [8] that all models of 
$\text {CT}^-$
carry a partial inductive truth predicate. Finally, we construct a partial truth predicate defined for a set of formulae whose syntactic depth forms a nonstandard cut which cannot be extended to a full truth predicate satisfying 
$\text {CT}^-$
.
