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Hieronymi, Philipp van den Dries, Lou Tserunyan, Anush Walsberg, Erik Caulfield, Erin 2018-09-27T16:17:42Z 2018-09-27T16:17:42Z 2018-07-09 2018-08 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. Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2018-09-27 without embargo terms The student, Erin Caulfield, accepted the attached license on 2018-07-06 at 15:27. The student, Erin Caulfield, submitted this Dissertation for approval on 2018-07-06 at 15:54. This Dissertation was approved for publication on 2018-07-09 at 11:00. DSpace SAF Submission Ingestion Package generated from Vireo submission #12762 on 2018-09-27 at 10:47:06 Made available in DSpace on 2018-09-27T16:17:42Z (GMT). No. of bitstreams: 3 CAULFIELD-DISSERTATION-2018.pdf: 988369 bytes, checksum: 7de9c57bd1c6c3b5e45319d320ec299d (MD5) LICENSE.txt: 4211 bytes, checksum: 71237396655b6d752d93c6d238e5c131 (MD5) PROQUEST_LICENSE.txt: 4557 bytes, checksum: d31c937edb21518dfe53abb3aab3b46f (MD5) Previous issue date: 2018-07-09 application/pdf http://hdl.handle.net/2142/101541 en Copyright 2018 Erin Caulfield Expansions of the real field Complex subgroups Model theory Classifying expansions of the real field by complex subgroups text text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.