Archivierte Veranstaltungen Detail

Vortragende Person/Vortragende Personen:
Floris Vermeulen

Shortly after the invention of o-minimality, it was observed by van den Dries that work by Gabrielov proves the o-minimality of the real field with restricted analytic functions. In the eighties, Denef and van den Dries simplify this proof through the usage of Weierstrass division. Since then, this Weierstrass division has played a central role in understanding the model theory of fields with analytic structure. In fact, it forms the key component of the general framework of Cluckers and Lipshitz for fields with analytic structure, both for real closed fields and for valued fields. One of the main results of Cluckers-Lipshitz is that real closed fields with analytic structure are o-minimal.

I will give a general introduction to the framework of Cluckers-Lipshitz for ordered fields, before showing how to move beyond real closed fields and treat almost real closed fields with analytic structure. We show that such structures are also geometrically tame, namely they are h-minimal when equipped with the natural valuation. We also have a precise description of the structure on the residue field and the value group. This is joint work with Kien Huu Nguyen and Mathias Stout.