Eliana Bariga will speak about Definably compact semialgebraic groups over real closed fields.
Abstract: Semialgebraic groups over a real closed field can be seen as a generalization of the semialgebraic groups over the real field, and also as a particular case of the groups definable in an o-minimal structure.
OAntongiulio Fornasiero will speak about definable and interpretable groups and fields in the p-adics.
Abstract: A. Pillay showed that every definable group in the p-adics has a canonical topology and differential structure, and deduced that every definable field is either finite or a finite extension of Q_p. In a joint work with J. de la Nuez Gonzalez we extend the analysis to interpretable fields, and show that they are either countable or finite extensions of Q_p.
I will define the notions described in the title, and ask if they are equivalent. I will present a proof showing that they are in case the theory is NIP. The proof is essentially the proof of the fact that the lack of distality is witnessed by a sequence of singletons by Pierre Simon’s.
Fixing a complete first order theory T, countable for transparency, we had known quite well for which cardinals T has a saturated model. This depends on T of course - mainly of whether it is stable/super-stable. But the older, precursor notion of having a universal notion lead us to more complicated answer, quite partial so far, e.g the strict order property and even SOP_4 lead to having "few cardinals" (a case of GCH almost holds near the cardinal). Note that eg GCH gives a complete