Hahn Field Representation of A. Robinson's Asymptotic Numbers

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Let *R be a nonstandard extension of R and ρ be a positive infinitesimal in *R. We show how to create a variety of isomorphisms between A. Robinson's field of asymptotic numbers ρR and the Hahn field ρR(tʳ), where ρR is the residue class field of ρR. Then, assuming that *R is fully saturated we show that ρR is isomorphic to *R and so ρR contains a copy of *R. As a consequence (that is important for applications in non-linear theory of generalized functions) we show that every two fields of asymptotic numbers corresponding to different scales are isomorphic.