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Comparing various concepts of function prediction. Part 2.
(Latvia State University, 1975)
Prediction: f(m+1) is guessed from given f(0), ..., f(m). Program synthesis: a program computing f is guessed from given f(0), ..., f(m). The hypotheses are required to be correct for all sufficiently large m, or with some ...
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 ...