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Title:Algebraically closed fields with characters; differential-henselian monotone valued differential fields
Author(s):Hakobyan, Tigran
Director of Research:van den Dries, Lou
Doctoral Committee Chair(s):Hieronymi, Philipp
Doctoral Committee Member(s):Tserunyan, Anush; Walsberg, Erik
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):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
Abstract: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.
Issue Date:2018-06-29
Type:Thesis
URI:http://hdl.handle.net/2142/101483
Rights Information:Copyright 2018 Tigran Hakobyan
Date Available in IDEALS:2018-09-27
Date Deposited:2018-08


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