2026/2027

Filters and Ultrafilters

Type: Optional course (faculty)

Delivered by: Faculty of Mathematics

Where: Faculty of Mathematics

When: 1, 2 module

Open to: students of all HSE University campuses

Instructors: Alexander Zapryagaev

Language: English

ECTS credits: 3

Contact hours: 30

Course Syllabus

Abstract

The language of filters and ultrafilters permeates all branches of mathematics, enabling the discovery of analogies and profound correspondences between results from various disciplines. Such diverse phenomena as the representation of Boolean algebras, the compactness of first-order logic, and the existence of maximal ideals can be unified into a common framework using ultrafilters. In this course, we will learn to use filters, ultrafilters, and ultrapowers, as well as the dual concept of nets, the latter naturally generalizing the familiar notion of a sequence from mathematical analysis.