Submission date: 31 October 2016

Abstract:

Truncation in Generalized Series fields is a robust notion, in the sense that it is preserved under various algebraic and some transcendental extensions. In this paper, we study conditions that ensure that a truncation closed set extends naturally to a truncation closed differential ring, and a truncation closed differential field has a truncation closed Liouville closure. In particular, we introduce the Notion of IL-closedness in Unions of Hahn fields in order to determine that this condition is sufficient to preserve truncation in those two settings for constructions such as the field of logarithmic-exponential transseries.

Mathematics Subject Classification: 34C05, 40J99, 16W60

Keywords and phrases:

Full text arXiv 1610.10058: pdf, ps.