 Gödel’s incompleteness theorems pose very difficult problems for Carnap in this and other regards. The first incompleteness theorem tells us that in any \((\omega\)-) consistent formal theory whose theorems are recursively enumerable and which entails a certain (rather limited) amount of arithmetic, there will be an arithmetical sentence such that neither it nor its negation is provable. In Carnap’s terminology, this seems to yield non-determinate sentences, which is a problem for him if we are convinced that nonetheless some of these sentences are true; and indeed the key type of sentences used to prove the incompleteness result—‘Gödel sentences’—are in fact true in the standard model of arithmetic if these sentences are constructed in an appropriate way (there are different ways of doing this) from a theory itself true in that model.