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

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

Hakobyan, Tigran

关键词: 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;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/101483/HAKOBYAN-DISSERTATION-2018.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

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.