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10 votes
0 answers
274 views

Open problems in complete theories

It is well-known that every complete recursively enumerable first-order theory is decidable. Does that mean that such theories are "trivial", or are there still interesting open problems ...
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17 votes
7 answers
2k views

Non-constructive proofs of decidability?

Are there examples of sets of natural numbers that are proven to be decidable but by non-constructive proofs only?