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Higher type recursion for transfinite machine theory. (English) Zbl 1434.03113

Manea, Florin (ed.) et al., Computing with foresight and industry. 15th conference on computability in Europe, CiE 2019, Durham, UK, July 15–19, 2019. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 11558, 72-83 (2019).
Summary: We look at some preliminary work in the theory of transfinite Turing machines generalised in the manner of Kleene to higher type recursion theory. The underlying philosophy is that ordinary Turing computability and inductive definability is replaced by the example here of infinite time Turing machine computability and quasi-inductive definability.
For the entire collection see [Zbl 1428.68037].

MSC:

03D65 Higher-type and set recursion theory
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