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The double-incompleteness theorem
(Stiinca, Kishinev, 1976)
Let T be a strong enough theory, and M - its metatheory, both are consistent. Then there is a closed arithmetical formula H that is undecidable in T, but one cannot prove in M neither that H is T-unprovable, nor that H is ...
The double-incompleteness theorem
(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 ...