Résume  A divisible ordered abelian group is an exponential group if its rank as an ordered set is isomorphic to its negative cone. Exponential groups appear as the value groups of ordered exponential fields, and were studied in [1]. In [2] we gave an explicit construction of exponential groups as Hahn groups of series with support bounded in cardinality by an uncountable regular cardinal kappa. An explog series s is said to be log atomic if the nthiterate of log(s) is a monomial for all n in N. In this talk I will present a modified construction of kappabounded Hahn groups and exploit it to construct kappa bounded Hahn fields without logatomic elements. This is ongoing joint work with Berarducci, Mantova and Matusinski.
[1] S. Kuhlmann, Ordered exponential fields, The Fields Institute Monograph Series, vol 12. Amer. Math. Soc. (2000)
[2] S. Kuhlmann and S. Shelah, Kappabounded ExponentialLogarithmic power series fields, Annals Pure and Applied Logic, 136, 284296 (2005)
