Решетка определимости. Источники и направления исследований
Аннотация
В статье представлены результаты и открытые проблемы, относящиеся к пространствам определимости (редуктам), а также источникам этой области, начиная с XIX века. Исследуются условия конечности и ограничения, в том числе глубина чередования кванторов и число аргументов. Описаны результаты, относящиеся к описанию решеток
пространств определимости для числовых и других естественных структур. Методы исследования включают изучение групп автоморфизмов элементарных расширений рассматриваемых структур, использование теоремы Свенониуса
Об авторах
Алексей Львович Семенов
Московский государственный университет им. М. В. Ломоносова, Институт кибернетики и образовательной информатики им. А. И. Берга ФИЦ ИУ РАН
Россия
Россия
Сергей Федорович Сопрунов
Центр педагогического мастерства Департамента образования и науки Москвы, Институт кибернетики и образовательной информатики им. А. И. Берга ФИЦ ИУ РАН
Россия
Россия
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При поддержке: Работа выполнена при поддержке РНФ (А. Л. Семенов, грант № 17-11-01377 – разделы 1, 3, 5) и РФФИ (С. Ф. Сопрунов, грант № 19-29-14199 – разделы 2, 4)
Для цитирования:
Семенов А.Л., Сопрунов С.Ф. Решетка определимости. Источники и направления исследований. Чебышевский сборник. 2021;22(1):304-327. https://doi.org/10.22405/2226-8383-2021-22-1-304-327
For citation:
Semenov A.L., Soprunov S.F. The lattice of definability. Origins and Directions of Research. Chebyshevskii Sbornik. 2021;22(1):304-327. (In Russ.) https://doi.org/10.22405/2226-8383-2021-22-1-304-327
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