Algebraically closed fields with characters; differential-henselian monotone valued differential fields

This thesis consists of two unrelated research projects. In the first project we study the model theory of the 2-sorted structure (F, C; χ), where F is an algebraic closure of a finite field of characteristic p, C is the field of complex numbers and χ ∶ F → C is an injective, multiplication preserving map. In the second project we study the model theory of the differential-henselian monotone valued differential fields. We also consider definability in differential-henselian monotone fields with c-map and angular component map.

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

• Hakobyan, Tigran

Contributors dc:contributor

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

• mathematical logic
• model theory
• quantifier elimination
• NIP
• fields
• algebraically closed fields
• characters
• differential fields
• valued fields
• valued differential fields
• d-henselian fields
• monotone valued differential fields
• Ax-Kochen-Ershov principle
• Ax-Kochen principle

Statement dc:rights

• Copyright 2018 Tigran Hakobyan

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/101483

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/101483