Truncation in differential Hahn fields

Being closed under truncation for subsets of generalized series fields is a robust property in the sense that it is preserved under various algebraic and transcendental extension procedures. Nevertheless, in Chapter 4 of this dissertation we show that generalized series fields with truncation as an extra primitive yields undecidability in several settings. Our main results, however, concern the robustness of being truncation closed in generalized series fields equipped with a derivation, and under extension procedures that involve this derivation. In the last chapter we study this in the ambient field T of logarithmic-exponential transseries. It leads there to a theorem saying that under a natural ``splitting'' condition the Liouville closure of a truncation closed differential subfield of T is again truncation closed.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2018

Author dc:creator

• Camacho Ahumada, Santiago

Contributors dc:contributor

• Hieronymi, Philipp
• Tserunyan, Anush
• Walsberg, Erik
• van den Dries, Lou

• Valued Fields
• Transseries
• Truncation
• Differential Algebra
• Hahn Fields

Statement dc:rights

• Copyright 2018 Santiago Camacho Ahumada

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/100890

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/100890