University of Illinois Urbana-Champaign

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

Hakobyan, Tigran

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

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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http://hdl.handle.net/2142/101483
Copyright and License Information
Copyright 2018 Tigran Hakobyan

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