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Processes and Structures on Approximation Spaces

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Algebra and Logic Aims and scope

We introduce the concept of a computability component on an admissible set and consider minimal and maximal computability components on hereditarily finite superstructures as well as jumps corresponding to these components. It is shown that the field of real numbers Σ-reduces to jumps of the maximal computability component on the least admissible set ℍ𝔽(∅). Thus we obtain a result that, in terms of Σ-reducibility, connects real numbers, conceived of as a structure, with real numbers, conceived of as an approximation space. Also we formulate a series of natural open questions.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    A. I. Stukachev

  2. Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090, Russia

    A. I. Stukachev

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  1. A. I. Stukachev
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Correspondence to A. I. Stukachev.

Additional information

Supported by the Russian Ministry of Education and Science (project No. 8227), by RFBR (project No. 15-01-05114), and by the Grants Council (under RF President) for State Aid of Leading Scientific Schools (grant NSh-6848.2016.1).

Translated from Algebra i Logika, Vol. 56, No. 1, pp. 93-109, January-February, 2017.

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Stukachev, A.I. Processes and Structures on Approximation Spaces. Algebra Logic 56, 63–74 (2017). https://doi.org/10.1007/s10469-017-9426-9

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  • DOI: https://doi.org/10.1007/s10469-017-9426-9

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