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

Hakobyan, Tigran

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Description

Title

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

Author(s)

Hakobyan, Tigran

Issue Date

2018-06-29

Director of Research (if dissertation) or Advisor (if thesis)

van den Dries, Lou

Doctoral Committee Chair(s)

Hieronymi, Philipp

Committee Member(s)

• Tserunyan, Anush
• Walsberg, Erik

Department of Study

Mathematics

Discipline

Mathematics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(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.

Graduation Semester

2018-08

Type of Resource

text

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Copyright and License Information

Copyright 2018 Tigran Hakobyan

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