On strongly minimal Steiner geometries Annotation. Steiner systems are an interesting mathematical object that has been
studied since the middle of the 19th century. At first, only finite Steiner systems were studied,
the study of a possible finite number of its elements was an interesting task for combinatorics. D.
Baldwin and G. Paolini constructed a family of infinite Steiner systems whose elementary theory
is strongly minimal. D. Baldwin and W. Werbowski proved that these strongly minimal Steiner
systems do not admit the elimination of imaginary elements. We construct a variant of the
strongly minimal Steiner system that admits the elimination of imaginary elements.
Keywords: strongly minimal theory, Steiner system, elimination of imaginaries, Fraisse–
Hrushovski construction.
List of literature: 1.
Baldwin J., Paolini G. Strongly Minimal Steiner Systems I: Existence // The Journal of
Symbolic Logic. — 2021. — V. 86(4). — P. 1486–1507.
2.
HrushovskiE. A new strongly minimal set // Annals of Pure and Applied Logic. —
1993. — Vol. 62. — P. 147–166.
3.
Baldwin J.,Verbovskiy V. Towards a Finer Classification of Strongly Minimal Sets //
Preprint. —
https://arxiv.org/abs/2106.15567
.
Университеттің 85 жылдығына арналған «Қазіргі заманғы математика: проблемалары және қолданыстары» III халықаралық Тайманов оқуларының материалдар жинағы, 25 қараша, 2022 жыл 19
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СВОЙСТВА МОМЕНТНЫЕ НОРМ В НЕКОТОРЫХ ПРОСТРАНСТВАХ ОРЛИЧА Е.А.АБЖАНОВ - кандидат физико-математических наук, А.Ж.МАДЕЛХАНОВА -
