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October 19, 2026
'Cultural Studies Seeks to Understand What Lies Beneath the Surface of Everyday Things'
Maxim Zhiganov has been exploring different aspects of sound for many years—first in relation to his native Perm and then on a broader, global scale. In this interview for the HSE Young Scientists project, he talks about sound maps, the special issue of the journal Logos, and why it is important to make the familiar less clear and obvious.
October 14, 2026
At HSE University–St Petersburg, Experts Discuss How AI Changes Tourist Routes and Cultural Heritage
Neural networks are no longer simple travel assistants; now they decide what to include on the route and what to skip. Artificial intelligence changes how people perceive a place and shapes the image of tourist centres. At the II International Scientific and Practical Conference ’Information Technologies in the Preservation and Promotion of Cultural Heritage,’ researchers discussed who controls algorithmic solutions and in what ways, and whether authentic traditions get lost in them.
October 12, 2026
Road Injuries Leading Cause of Death Among Men Aged 10 to 39
Worldwide, road injuries are the leading cause of death among males aged 10–39. An international team of researchers reached this conclusion as part of the Global Burden of Disease Study 2023, analysing data from 204 countries between 1990 and 2023. Their findings have been published in The Lancet Public Health, with HSE University Professor Vasily Vlassov listed among the collaborators.

 

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О ДВУХ РАЗЛИЧНЫХ ТИПАХ ОРДИНАЛЬНЫХ ИТЕРАЦИЙ ВНУТРЕННИХ ФУНКТОРОВ

С. 134–139.
Polyakov N. L.

In [1], the concept of a skew limit ultrapower of ordinal rank of an arbitrary model $\mathfrak M$ with respect to an ultrafilter $\mathfrak u$ was introduced for a model-theoretic characterization of some natural preorders on the set of ultrafilters on the set $\beta\omega$. We will show that this concept admits broad generalizations that can be defined in terms of category theory.

Language: Russian
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Keywords: ultrafilterультрафильтрRudin-Keisler preorderultrapowerlimit ultrapowerпредпорядок Рудин-Кейслераультрастепеньпредельная ультрастепень

In book

Algebra and model theory 2025. Volume 16
Algebra and model theory 2025. Volume 16
., 2025.
Similar publications
Solution to Hart–van Mill’s problem 61
Polyakov N. L., Saveliev D. I., Russian Mathematical Surveys 2026 Vol. 81 No. 1 P. 205–206
We solve Problem 61 from Hart and van Mill’s list on whether every finite partial order is embeddable in the Rudin–Keisler order on (types of) ultrafilters over $\omega$. ...
Added: January 31, 2026
On embedding of partially ordered sets in $(\beta\omega, \leq_{RK})$
Polyakov N. L., Saveliev D., Working papers by Cornell University. Series math "arxiv.org" 2025 P. 1–13
A natural question, which appeared as Problem 61 in Hart and van Mill's list of open problems on  (2024), asks whether every finite partial order is embeddable in the Rudin--Keisler order on (types of) ultrafilters over a countable set. Although the positive answer, even for all countable partial orders, was proved under CH in Blass' thesis ...
Added: November 25, 2025
Generalizations of the Rudin - Keisler preorder and their model-theoretic applications
N. L. Poliakov, Saveliev D., Bulletin of L.N. Gumilyov Eurasian National University. Mathematics, computer science, mechanics series 2025 Vol. 151 No. 2 P. 6–11
Generalizing of the Rudin--Keisler preorder, we introduce relations $R_\alpha$     (and $R_{<\alpha}$) on the set $\scc\omega$ of ultrafilters on~$\omega$. They     form an ordinal sequence of length~$\omega_1$ which is strictly increasing by     inclusion and lies between the Rudin--Keisler preorder and the Comfort preorder.     We show that the composition of these relations is expressed ...
Added: July 16, 2025
Об одном комбинаторном приложении теории ультрафильтров: новая конструкция графов без треугольников и с произвольно большим хроматическим числом
Polyakov N. L., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2025 Т. 522 № 1 С. 40–49
The paper describes a new method for constructing graphs without triangles and with an arbitrarily large chromatic number. The properties of various types of ultrafilter extensions of functions and predicates are used to justify the method. ...
Added: June 3, 2025
Ультрарасширения инфинитарных функций
Polyakov N. L., В кн.: Международная конференция МАЛЬЦЕВСКИЕ ЧТЕНИЯ 13–17 ноября 2023 г. Тезисы докладов.: [б.и.], 2023. С. 104–104.
Added: November 30, 2024
On the RK-preorder on C-cones of RK-minimal ultrafilters
N. L. Polyakov, , in: Model Theory and Algebra 2024.: -, 2024. P. 87–92.
We describe the Rudin-Keisler preorder on lower cones with respect to the Comfort preorder of Ramsey ultrafilters ...
Added: November 18, 2024
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