Ak. god. 2026./2027.

In this talk, we shall discuss the foundations of mathematics based on the von Neumann–Bernays–Gödel (NBG) theory of sets and classes. We will provide a rigorous definition of a mathematical structure and classify these structures both by their complexity and by their capacity to treat canonical sets and classes (such as the sets of integers, rationals, reals, and complex numbers, or the proper classes of cardinals, ordinals, and surreal numbers). Furthermore, we shall distinguish atomic mathematical structures that complete Bourbaki’s three “mother structures” (order, magma, and topology), and conclude with a discussion of some interesting mathematical structures on proper classes.