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We introduce a principle of local collection for compositional truthpredicates and show that it is conservative over the classically compositionaltheory of truth in the arithmetical setting. This axiom states that uponrestriction to formulae of any syntactic complexity, the resulting predicatesatisfies full collection. In particular, arguments using collection for thetruth predicate applied to sentences occurring in any given (code of a) proofdo not suffice to show that the conclusion of that proof is true, in starkcontrast to the case of induction scheme. We analyse various further resultsconcerning end-extensions of models of compositional truth and the collectionscheme for the compositional truth predicate.

Local collection scheme and end-extensions of models of compositional truth