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#### What is Mathematics: Gödel's Theorem and Around (Edition 2013)

(2013-06-23)

Hyper-textbook for students in mathematical logic and foundations of mathematics. Edition 2013. ATTENTION! New Edition 2015 available at https://dspace.lu.lv/dspace/handle/7/5306.

#### 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 ...