University of Illinois Urbana-Champaign

Classifying expansions of the real field by complex subgroups

Caulfield, Erin

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https://hdl.handle.net/2142/101541

Description

Title
Classifying expansions of the real field by complex subgroups
Author(s)
Caulfield, Erin
Issue Date
2018-07-09
Director of Research (if dissertation) or Advisor (if thesis)
Hieronymi, Philipp
Doctoral Committee Chair(s)
van den Dries, Lou
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)
  • Expansions of the real field
  • Complex subgroups
  • Model theory
Abstract
In this thesis, we study expansions of the real field by multiplicative subgroups of the complex numbers. We first consider expansions by a subgroup generated by an element of the unit circle and a positive real number. We then consider expansions by a subgroup generated by a complex number and a positive real number. In both of these cases, we investigate the sets definable in these structures and their open cores.
Graduation Semester
2018-08
Type of Resource
text
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http://hdl.handle.net/2142/101541
Copyright and License Information
Copyright 2018 Erin Caulfield

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