Order positive fields. I Full article
| Journal |
Algebra and Logic
ISSN: 0002-5232 , E-ISSN: 1573-8302 |
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| Output data | Year: 2023, Volume: 62, Number: 3, Pages: 203-214 Pages count : 12 DOI: 10.1007/s10469-024-09738-1 | ||||
| Tags | strictly ordered fields, positive structures, computable real numbers | ||||
| Authors |
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| Affiliations |
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Funding (3)
| 1 | Russian Science Foundation | 23-11-00170 |
| 2 | Sobolev Institute of Mathematics | FWNF-2022-0011 |
| 3 | Yershov Institute of Informatic Systems | FWNU-2021-0003 |
Abstract:
The notion of a computable structure based on numberings with decidable equality is well established with a number of prominent results. Nevertheless, applied to strictly ordered f ields, it fails to capture some natural properties and constructions for which decidability of equality is not assumed. For example, the field of primitive recursive real numbers is not computable, and there exists a computable real closed field with noncomputable maximal Archimedean subfields. We introduce thenotionofanorderpositivefieldwhich aims to overcome these limitations. A general criterion is presented which decides when an Archimedean field is order positive. Using this criterion, we show that the field of primitive recursive real numbers is order positive and that the Archimedean parts of order positive real closed fields are order positive. We also state a program for further research.
Cite:
Korovina M.V.
, Kudinov O.V.
Order positive fields. I
Algebra and Logic. 2023. V.62. N3. P.203-214. DOI: 10.1007/s10469-024-09738-1 WOS Scopus РИНЦ OpenAlex
Order positive fields. I
Algebra and Logic. 2023. V.62. N3. P.203-214. DOI: 10.1007/s10469-024-09738-1 WOS Scopus РИНЦ OpenAlex
Original:
Коровина М.В.
, Кудинов О.В.
Порядково позитивные поля. I
Алгебра и логика. 2023. Т.62. №3. С.307-322. DOI: 10.33048/alglog.2023.62.301 РИНЦ
Порядково позитивные поля. I
Алгебра и логика. 2023. Т.62. №3. С.307-322. DOI: 10.33048/alglog.2023.62.301 РИНЦ
Dates:
| Submitted: | Apr 21, 2023 |
| Accepted: | Apr 10, 2024 |
| Published print: | Apr 22, 2024 |
| Published online: | Apr 22, 2024 |
Identifiers:
| Web of science: | WOS:001205944600001 |
| Scopus: | 2-s2.0-85191061720 |
| Elibrary: | 67058863 |
| OpenAlex: | W4395007994 |
Citing:
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