#### Abstract for the paper

## Elementary properties of power series fields over finite fields

* by Franz-Viktor Kuhlmann, Saskatoon*

In spite of the analogies between Q_p and F_p((t)) which became
evident through the work of Ax and Kochen, an adaptation of the complete
recursive axiom system given by them for Q_p to the case of
F_p((t)) does not render a complete axiom system. We show the
independence of elementary properties which express the action of
additive polynomials as maps on F_p((t)). We formulate an elementary
property expressing this action and show that it holds for all maximal
valued fields. We also derive an example of a rather simple immediate
valued function field over a henselian defectless ground field which is
not a henselian rational function field. This example is of special
interest in connection with the open problem of local uniformization in
positive characteristic.

*Last update: November 15, 1999*