Abstract
We consider an approach to computability in admissible sets based on a general notion of computable process, with Σ-predicates and Σ-operators as special cases, inspired by ideas from the Ershov-Scott theory of approximation spaces. We present some results from different topics in generalized computability, including reducibilities on admissible sets and structures, general notion of a jump, and computable analysis (more exactly, computability over the reals), obtained with the help of this approach, and state some open questions.
This work was supported by the Ministry of Education and Science of Russian Federation (project 8227), the Russian Foundation for Basic Research (grants 11-01-00688-a, 13-01-91001-ANF-a), and the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (grant N.Sh.-276.2012.1).
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Stukachev, A. (2013). On Processes and Structures. In: Bonizzoni, P., Brattka, V., Löwe, B. (eds) The Nature of Computation. Logic, Algorithms, Applications. CiE 2013. Lecture Notes in Computer Science, vol 7921. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39053-1_46
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DOI: https://doi.org/10.1007/978-3-642-39053-1_46
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