Each effectively generated system has its own Gödel sentence. It is possible to define a larger system "F’" that contains the whole of "F" plus "G""F" as an additional axiom. This will not result in a complete system, because Gödel's theorem will also apply to "F’", and thus "F’" also cannot be complete. In this case, "G""F" is indeed a theorem in "F’", because it is an axiom. Because "G""F" states only that it is not provable in "F", no contradiction is presented by its provability within "F’". However, because the incompleteness theorem applies to "F’", there will be a new Gödel statement "G""F′" for "F’", showing that "F’" is also incomplete. "G""F′" will differ from "G""F" in that "G""F′" will refer to "F’", rather than "F".