The double-incompleteness theorem - Podnieks, Karlis (Latvia State University, 1975)
Let T be a theory, Q - a metatheory of T. Under certain conditions there exist T-undecidable sentences for which this undecidability cannot be proved in Q. For English translation and proof, see K. Podnieks What is mathematics: Godel's theorem and around.
Keywords: double incompleteness; incompleteness; incompleteness theorem