INTERPRETING A FIELD IN ITS HEISENBERG GROUP Научная публикация
Журнал |
Journal of Symbolic Logic
ISSN: 0022-4812 |
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Вых. Данные | Год: 2022, Том: 87, Номер: 3, Страницы: 1215-1230 Страниц : 16 DOI: 10.1017/jsl.2021.107 | ||||||||||||||||
Ключевые слова | Computability; computable structure theory; Heisenberg group of a field; interpretation; parameters | ||||||||||||||||
Авторы |
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Организации |
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Реферат:
We improve on and generalize a 1960 result of Maltsev. For a field F, we denote by the Heisenberg group with entries in F. Maltsev showed that there is a copy of F defined in, using existential formulas with an arbitrary non-commuting pair of elements as parameters. We show that F is interpreted in using computable formulas with no parameters. We give two proofs. The first is an existence proof, relying on a result of Harrison-Trainor, Melnikov, R. Miller, and Montalbán. This proof allows the possibility that the elements of F are represented by tuples in of no fixed arity. The second proof is direct, giving explicit finitary existential formulas that define the interpretation, with elements of F represented by triples in. Looking at what was used to arrive at this parameter-free interpretation of F in, we give general conditions sufficient to eliminate parameters from interpretations.
Библиографическая ссылка:
Alvir R.
, Calvert W.
, Goodman G.
, Harizanov V.
, Knight J.
, Miller R.
, Morozov A.
, Soskova A.
, Weisshaar R.
INTERPRETING A FIELD IN ITS HEISENBERG GROUP
Journal of Symbolic Logic. 2022. V.87. N3. P.1215-1230. DOI: 10.1017/jsl.2021.107 WOS Scopus РИНЦ OpenAlex
INTERPRETING A FIELD IN ITS HEISENBERG GROUP
Journal of Symbolic Logic. 2022. V.87. N3. P.1215-1230. DOI: 10.1017/jsl.2021.107 WOS Scopus РИНЦ OpenAlex
Даты:
Опубликована online: | 23 дек. 2021 г. |
Идентификаторы БД:
Web of science: | WOS:000847361900017 |
Scopus: | 2-s2.0-85121898458 |
РИНЦ: | 47903983 |
OpenAlex: | W4205228190 |