Computer Science – Logic in Computer Science
Scientific paper
2006-03-17
Computer Science
Logic in Computer Science
submitted to Journal of Complexity
Scientific paper
In the BCSS model of real number computations we prove a concrete and explicit semi-decidable language to be undecidable yet not reducible from (and thus strictly easier than) the real Halting Language. This solution to Post's Problem over the reals significantly differs from its classical, discrete variant where advanced diagonalization techniques are only known to yield the existence of such intermediate Turing degrees. Strengthening the above result, we construct (that is, obtain again explicitly) as well an uncountable number of incomparable semi-decidable Turing degrees below the real Halting problem in the BCSS model. Finally we show the same to hold for the linear BCSS model, that is over (R,+,-,<) rather than (R,+,-,*,/,<).
Meer Klaus
Ziegler Martin
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