Hahn Field Representation of A. Robinson's Asymptotic Numbers
| dc.creator | Todorov, Todor | |
| dc.creator | Wolf, Robert | |
| dc.date | 2006-01-30 | |
| dc.date.accessioned | 2026-07-07T06:59:27Z | |
| dc.date.available | 2026-07-07T06:59:27Z | |
| dc.description | Let $^*\mathbb{R}$ be a nonstandard extension of $\mathbb{R}$ and $ρ$ be a positive infinitesimal in $^*\mathbb{R}$. We show how to create a variety of isomorphisms between A. Robinson's field of asymptotic numbers $^ρ\mathbb{R}$ and the Hahn field $\hat{^ρ\mathbb{R}}(t^\mathbb{R})$, where $\hat{^ρ\mathbb{R}}$ is the residue class field of $^ρ\mathbb{R}$. Then, assuming that $^*\mathbb{R}$ is fully saturated we show that $\hat{^ρ\mathbb{R}}$ is isomorphic to $^*\mathbb{R}$ and so $^ρ\mathbb{R}$ contains a copy of $^*\mathbb{R}$. 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. | |
| dc.description | 18 pages | |
| dc.identifier | https://arxiv.org/abs/math/0601722 | |
| dc.identifier | http://arxiv.org/abs/math/0601722 | |
| dc.identifier | Nonlinear Algebraic Analysis and Applications (ICGF 2000), 2004 CSP, p.357-374. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107753 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Logic | |
| dc.subject | 03H05, 06A05, 12J10, 12J25, 13A18, 16W60 | |
| dc.title | Hahn Field Representation of A. Robinson's Asymptotic Numbers | |
| dc.type | text |