SURREAL ORDERED EXPONENTIAL FIELDS

The Exponential-Logarithmic Equivalence Classes of Surreal Numbers

In his monograph [Gon86], H. Gonshor showed that Conway’s real closed field of surreal numbers carries an exponential and logarithmic map. Subsequently, L. van den Dries and P. Ehrlich showed in [vdDE01] that it is a model of the elementary theory of the field of real numbers with the exponential function. In this paper, we give a complete description of the exponential equivalence classes (see...

Integration on Surreal Numbers

The thesis concerns the (class) structure No of Conway’s surreal numbers. The main concern is the behaviour on No of some of the classical functions of real analysis, and a definition of integral for such functions. In the main texts on No, most definitions and proofs are done by transfinite recursion and induction on the complexity of elements. In the thesis I consider a general scheme of defi...

On Partly Ordered Fields

Ordered Rings and Fields

Real closed exponential fields

In an extended abstract [20], Ressayre considered real closed exponential fields and integer parts that respect the exponential function. He outlined a proof that every real closed exponential field has an exponential integer part. In the present paper, we give a detailed account of Ressayre’s construction. The construction becomes canonical once we fix the real closed exponential field R, a re...