# 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.