Elementary properties of power series fields over finite fields

In spite of the analogies between Q(p) and F-p ((t)) which became evident t hrough the work of An and Kochen. an adaptation of the complete recursive a xiom system given by them For Q(p) to the case F-p ((t)) does not render a complete axiom system. We show the independence of elementary properties wh ich express the action of additive polynomials as maps on F-p((t)). We form ulate 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 w hich is not a henselian rational function field. This example is of special interest in connection with the open problem of local uniformization in po sitive characteristic.