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Set Theory

The theory of collections, from naive counting arguments to the axioms, cardinals and independence results that came out of them.

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A non-Noetherian local ring with finitely generated maximal ideal

2026NotesBogdan Zavyalov

A complete local ring with a finitely generated maximal ideal is Noetherian. Drop completeness and it fails: an ultraproduct construction gives a non-Noetherian local ring whose maximal ideal is principal.

Математический анализ 1. Лекция 1

2026LectureСтанислав Шапошников

Наивная теория множеств и парадокс Рассела, упорядоченная пара по Куратовскому и декартово произведение, функция как подмножество произведения, композиция, инъекции, сюръекции и биекции, группа биекций и вложение в неё любой группы, равномощность и индикаторы, теоремы Кантора–Бернштейна и Кантора.