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Решетка определимости. Источники и направления исследований

https://doi.org/10.22405/2226-8383-2021-22-1-304-327

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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


Сергей Федорович Сопрунов
Центр педагогического мастерства Департамента образования и науки Москвы, Институт кибернетики и образовательной информатики им. А. И. Берга ФИЦ ИУ РАН
Россия


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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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