Coloquio - Departamento de Matemáticas - Universidad Nacional

Lunes 16 de febrero - 4 pm
Edificio 405 Salón 202

Cardinal invariants of the continuum

Joerg Brendle - Universidad de Kobe (Japón)

Abstract: Cardinal invariants of the continuum are cardinal numbers which describe the combinatorial structure of the real line. Most of them assume values between the first uncountable cardinal aleph_1 and the cardinality of the continuum. Much of the motivation for studying such cardinals comes from problems in general topology, group theory etc. However, because of their strong interplay with forcing theory, they are also of intrinsic interest in set theory.

Most classical cardinal invariants are defined in terms of P(N) / fin (the quotient of the subsets of the natural numbers N by the finite sets), but recently cardinal invariants defined in terms of related structures have been investigated as well. For example, there is ongoing work on invariants related to P(C(H)), the collection of projections in the Calkin algebra C(H) (the quotient of the bounded operators on a separable Hilbert space by the compact operators).

In this talk, I will define some of the cardinal invariants, both for P(N) / fin and for P(C(H)), prove some basic results, and mention recent developments and open problems.