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Title:Classifying expansions of the real field by complex subgroups
Author(s):Caulfield, Erin
Director of Research:Hieronymi, Philipp
Doctoral Committee Chair(s):van den Dries, Lou
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):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.
Issue Date:2018-07-09
Type:Text
URI:http://hdl.handle.net/2142/101541
Rights Information:Copyright 2018 Erin Caulfield
Date Available in IDEALS:2018-09-27
Date Deposited:2018-08


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