Hahn Field Representation of A. Robinson's Asymptotic Numbers
Todor D. Todorov2006, arXiv (Cornell University)
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Abstract
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 ρ R and the Hahn field ρ R(t R ), where ρ R is the residue class field of ρ R. Then, assuming that * R is fully saturated we show that ρ R is isomorphic to * R and so ρ R 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.
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