On the Computability of Ordered Fields Full article
| Journal |
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports)
, E-ISSN: 1813-3304 |
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| Output data | Year: 2023, Volume: 20, Number: 2, Pages: 1341-1360 Pages count : 20 DOI: 10.33048/semi.2023.20.081 | ||||
| Tags | computable analysis, computability, index set, computable model theory, complexity. | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0011 |
Abstract:
In this paper we develop general techniques for structures of computable real numbers generated by classes of total computable (recursive) functions with special requirements on basic operations in order to investigate the following problems: whether a generated structure is a real closed field and whether there exists a computable copy of a generated structure. We prove a series of theorems that lead to the result that there are no computable copies for E_n-computable real numbers, where E_n is a level in Grzegorczyk hierarchy, n ≥ 3. We also propose a criterion of computable presentability of an archimedean ordered field.
Cite:
Korovina M.V.
, Kudinov O.V.
On the Computability of Ordered Fields
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2023. V.20. N2. P.1341-1360. DOI: 10.33048/semi.2023.20.081 Scopus РИНЦ
On the Computability of Ordered Fields
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2023. V.20. N2. P.1341-1360. DOI: 10.33048/semi.2023.20.081 Scopus РИНЦ
Dates:
| Submitted: | Aug 5, 2020 |
| Published print: | Nov 30, 2023 |
| Published online: | Nov 30, 2023 |
Identifiers:
| Scopus: | 2-s2.0-85179693345 |
| Elibrary: | 82134667 |
Citing:
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