 One should not get confused here: “Gödel’s theorem” is the general incompleteness result of Gödel which concerns a large class of formal systems, while the “Gödel sentence” is the constructed, formally undecidable sentence which varies from one formal system to another. This is why it is important to include the subscript \(F\) in \(G_F\). Furthermore, one should not confuse the two different senses of “undecidable” in this context. On the one hand, a particular sentence, like the Gödel sentence, may be undecidable in the sense of being independent, i.e., neither provable not refutable in a chosen system. On the other hand, a theory may be undecidable (see below) in the sense that there does not exist a decision method for determining of an arbitrary given sentence of the language whether or not it is derivable in the theory (so this latter sense of “undecidable” concerns, so to speak, an infinite class of statements).