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INTERPRETING A FIELD IN ITS HEISENBERG GROUP Научная публикация

Журнал

Journal of Symbolic Logic
ISSN: 0022-4812

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

Alvir R. ⁸ , Calvert W. ¹ , Goodman G. ⁷ , Harizanov V. ² , Knight J. ⁸ , Miller R. ^3,4 , Morozov A. ⁵ , Soskova A. ⁶ , Weisshaar R. ⁷

Организации

1	School of Mathematical and Statistical Sciences Mail Code 4408, Southern Illinois University, CARBONDALE, IL 62918, United States
2	Department of Mathematics, George Washington University, Usa E-mail: Harizanv@gwu.edu, WASHINGTON, DC 20052, United States
3	Mathematics DEPT., Queens College - Cuny, 65-30 KISSENA BLVD., QUEENS, NY 11367, United States
4	Programs in Mathematics and Computer Science, Cuny Graduate Center, 365 FIFTH AVENUE, NEW YORK, NY 10016, United States
5	Sobolev Institute of Mathematics Sb Ras, KOPTYUG AVE. 4, NOVOSIBIRSK, 630090, Russian Federation
6	DEPT. of Mathematical Logic Faculty of Math and COMP. Sci, Sofia University, 5 JAMES BOURCHIER BLVD. 1164, Sofia, Bulgaria
7	Department of Mathematics and Statistics, Wake Forest University, WINSTON-SALEM, NC 27101, United States
8	Department of Mathematics, University of Notre Dame, 255 HURLEY BLDG, NOTRE DAME, IN 46556, United States

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.

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

Опубликована online:

23 дек. 2021 г.

Web of science:	WOS:000847361900017
Scopus:	2-s2.0-85121898458
РИНЦ:	47903983
OpenAlex:	W4205228190

БД	Цитирований
Scopus	2
OpenAlex	1