Extra Session

There will be an extra talk by an invited speaker:

Professor Tobias Kaiser (Passau)

will speak on

Logarithms, constructible functions and integration on non-archimedean models of the theory of the real field with restricted analytic functions with value group of finite archimedean rank

  • Time: Friday, 06.03., 10:30 -- 12:00

  • Room: 25.22.O3.73

Abstract: We work in a model of the theory of the real field with restricted analytic functions such that its value group has finite archimedean rank. An example is given by the field of Puiseux series over the reals. We show how one can extend the restricted logarithm to a global logarithm with values in the polynomial ring over the model with dimension the archimedean rank. The logarithms are determined by algebraic data from the model, namely by a section of the model and by an embedding of the value group into its Hahn group. If the archimedean rank of the value group coincides with the rational rank the logarithms are equivalent. We illustrate how one can embed such a logarithm into a model of the real field with restricted analytic functions and exponentiation. This allows us to define constructible functions with good lifting properties. As an application we establish a full Lebesgue measure and integration theory with values in the polynomial ring.





April 2



April 9


Criteria for Regularity

April 16

no seminar

April 23


Construction of a Fundamental Solution

April 30


The Curve Selection Lemma

May 7


Localizations at Infinity

May 14


Description of the Wave Front Set

May 21


Hypoelliptic Operators

May 28


Introduction to O-Minimality

June 4


Why the class of subanalytic sets is (not) o-minimal

June 11

no seminar

June 18

no seminar

June 25

no seminar

July 2


From model completeness to o-minimality

July 9

no seminar

There will be an extra session with a guest somewhen in the winter term.


  • van den Dries, Lou: Tame Topology and O-minimal Structures

  • Hörmander, Lars: The Analysis of Linear Partial Differential Operators I

  • Hörmander, Lars: The Analysis of Linear Partial Differential Operators II


Anwendungen der Modelltheorie auf Partielle Differentialgleichungen



  • Ziel des ganzen

  • Grundlegende Begriffe: Distribution, Fouriertransformation, Fundamentallösung, Wellenfront


  • \(B_{p,k}\)-Räume

10.1.1.-10.1.15., hauptsächlich Definitionen und Lemmata analytischer Natur

Konstruktion einer Fundamentallösung

  • Existenzbeweis via Fouriertransformation

  • Regularität der konstruierten Lösung

7.3.10-7.3.12 und, technisch analytisch


  • Puiseuxreihe

  • Satz von Tarski-Seidenberg zitieren

  • Kurvenauswahlsatz

Anhang A oder eine andere Quelle, modelltheoretisch

Lokalisierungen im Unendlichen

  • Definition

  • Ein Approximationsergebnis

10.2.4.-10.2.10., (naiv) geometrisch und modelltheoretisch

Beschreibung der Wellenfront

  • Verwendung der Approximation aus dem vorigen Vortrag, um eine obere Abschätzung der Wellenfront zu geben

10.2.11.-10.2.13, analytisch diffizil

Hypoelliptische Operatoren

  • Begriff des hypoelliptischen Operators

  • Regularität von Nulllösungen

11.1.1.-11.1.4, zusammenfassen