Nonpresentability of Some Structures of Analysis in Hereditarily Finite Superstructures

A. S. Morozov

doi:10.1007/s10469-018-9468-7

Nonpresentability of Some Structures of Analysis in Hereditarily Finite Superstructures

A. S. Morozov

Кафедра дискретной математики и информатики ММФ и СУНЦ

Результат исследования: Научные публикации в периодических изданиях › статья › рецензирование

2 Цитирования (Scopus)

Аннотация

It is proved that any countable consistent theory with infinite models has a Σ-presentable model of cardinality 2^ω over. It is shown that some structures studied in analysis (in particular, a semigroup of continuous functions, certain structures of nonstandard analysis, and infinite-dimensional separable Hilbert spaces) have no simple Σ-presentations in hereditarily finite superstructures over existentially Steinitz structures. The results are proved by a unified method on the basis of a new general sufficient condition.

Язык оригинала	английский
Страницы (с-по)	458-472
Число страниц	15
Журнал	Algebra and Logic
Том	56
Номер выпуска	6
DOI	https://doi.org/10.1007/s10469-018-9468-7
Состояние	Опубликовано - 1 янв. 2018

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10.1007/s10469-018-9468-7

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