## APPLICATIONS OF TRANSFINITE SERIES TO INTEGERS AND REALS

## J. P. Ressayre (logic seminar)

Abstract:

I will sketch the following (connected) uses of transfinite series: 1)constructing various non standard models of Arithmetic 2)defining canonical asymptotic expansions for a wide class of real analytic functions 3)solving Hardy's problem on the inverse function of x.log x 4)proving that (R,E,exp) is o-minimal and model complete, whenever E is a family closed under derivations of restricted analytic function.