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Математическая логика, алгебра и теория чисел
On the computability of ordered fields
M. V. Korovina, O. V. Kudinov A.P. Ershov Institute of Informatics Systems, pr. Acad. Lavrentjev, 6, 630090, Novosibirsk, Russia
Аннотация:
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 $\mathcal{E}^n$-computable real numbers, where $\mathcal{E}^n$ is a level in Grzegorczyk hierarchy, $n\geq 3$. We also propose a criterion of computable presentability of an archimedean ordered field.
Ключевые слова:
computable analysis, computability, index set, computable model theory, complexity.
Поступила 5 августа 2020 г., опубликована 30 ноября 2023 г.
Образец цитирования:
M. V. Korovina, O. V. Kudinov, “On the computability of ordered fields”, Сиб. электрон. матем. изв., 20:2 (2023), 1341–1360
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/semr1644 https://www.mathnet.ru/rus/semr/v20/i2/p1341
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Страница аннотации: | 43 | PDF полного текста: | 9 | Список литературы: | 17 |
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