Das Wortproblem für Halbgruppen
Dienstag, 3.2.26, 14:30-16:00, SR 125
Minimal types and independence in differentially closed fields
Dienstag, 20.1.26, 14:30-16:00, SR 125
Working in the theory of differentially closed fields of characteristic 0, Fre- itag and Moosa introduced the degree of nonminimality d of a type as a measure of how many parameters are needed to witness that the type is not minimal. Together with Jaoui, they showed that if a stationary type has nonminimality degree \(d\ge 2\), weakly orthogonal and internal to the field of constants, its binding group acts generically \(d\)-transitively on the set of realizations of p. This can be used to show that if every triple of different realizations of a nonalgebraic stationary type is independent over its set of parameters, then the type is minimal.
The Proper Forcing Axiom Implies the Tree Property at \(\aleph_2\)
Dienstag, 11.11.25, 14:30-16:00, SR 125
Archimedean classes of hypernaturals, and their use in ART
Dienstag, 28.10.25, 14:30-16:00, Seminarraum 404
Arithmetic Ramsey Theory (ART) studies what kind of arithmetic configurations we cannot avoid taking a finite partition of the naturals: arithmetic progressions, large sets with all possible sums of their elements, solutions to certain polynomials are just some examples of these configurations (usually called Partition Regular, PR). How to deal with such problems? In the last years, ideas coming from nonstandard analysis - and linked with ultrafilter algebra - have provided a natural framework to study Ramsey-theoretic questions. In this talk, we will present a new tool to prove that certain polynomials are not PR: by adopting the nonstandard point of view, we will show how the notion of Archimedean classes of hypernaturals can easily produce negative results in ART. This is a joint work with Lorenzo Luperi Baglini.