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Computability is one of the fundamental notions of mathematics, trying to capture the effective content of mathematics. Starting from Gödel’s Incompleteness Theorem, it has now blossomed into a rich area with strong connections with other areas of mathematical logic as well as algebra and theoretical computer science.
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Klaus Ambos-Spies, Rodney G. Downey, Steffen Lempp, Wolfgang Merkle, Computability Theory. Oberwolfach Rep. 9 (2012), no. 1, pp. 397–455DOI 10.4171/OWR/2012/08