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van den Dries, Lou Hieronymi, Philipp Tserunyan, Anush Walsberg, Erik Hakobyan, Tigran 2018-09-27T16:17:24Z 2018-09-27T16:17:24Z 2018-06-29 2018-08 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. Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2018-09-27 without embargo terms The student, Tigran Hakobyan, accepted the attached license on 2018-06-25 at 13:13. The student, Tigran Hakobyan, submitted this Dissertation for approval on 2018-06-25 at 16:33. This Dissertation was approved for publication on 2018-06-29 at 10:02. DSpace SAF Submission Ingestion Package generated from Vireo submission #12611 on 2018-09-27 at 10:44:40 Made available in DSpace on 2018-09-27T16:17:24Z (GMT). No. of bitstreams: 4 HAKOBYAN-DISSERTATION-2018.pdf: 559980 bytes, checksum: 0d14a3e2453f887b35408c012b40f89b (MD5) Thesis - Tigran Hakobyan.zip: 91732 bytes, checksum: 2cad8ae2133200550b11360af0ae67d2 (MD5) LICENSE.txt: 4212 bytes, checksum: 289b1b0351de67a0c2565b35337f3e66 (MD5) PROQUEST_LICENSE.txt: 4558 bytes, checksum: af8bd922a20ee0ef89b0d8e422e26bc8 (MD5) Previous issue date: 2018-06-29 application/pdf http://hdl.handle.net/2142/101483 en Copyright 2018 Tigran Hakobyan 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 Algebraically closed fields with characters; differential-henselian monotone valued differential fields text text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.