Doklady MathematicsDoklady MathematicsДоклады Российской академии наук. Математика, информатика, процессы управления2686-95433034-5049The Russian Academy of Sciences69844210.7868/S3034504925050188MATHEMATICSМАТЕМАТИКАResearch ArticleON THE GALOIS CONNECTION FOR CLOSED CLASSES OF INFINITARY FUNCTIONSО соответствии галуа для замкнутых классов инфинитарных функцийPolyakovN. LПоляковН. Лproduktov@hse.ruShamolinM. VШамолинМ. В

Corresponding member of the RAS

член-корреспондент РАН

shamolin@imec.msu.ruHSE UniversityНациональный исследовательский университет “Высшая школа экономики”Moscow State University named after M. V. LomonosovМосковский государственный университет имени М. В. Ломоносова150920255251VOL 525, NO1 (2025)ТОМ 525, №1 (2025)13514310122025Copyright ©; 2025, Russian Academy of SciencesCopyright ©; 2025, Российская академия наук2025Russian Academy of SciencesРоссийская академия наукhttps://journals.eco-vector.com/2686-9543/article/view/698442

In this paper, Galois theory is developed for closed sets of functions of any ordinal arity. The classical theorem on Galois-closed classes of functions and sets of predicates on finite sets is transferred to the general case.

В работе развивается теория Галуа для замкнутых множеств функций любой ординальной ариости. Классическая теорема о галуа-замкнутых классах функций и множеств предикатов на конечных множествах переносится на общий случай.

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