Classifying expansions of the real field by complex subgroups

Expansions of the real field;Complex subgroups;Model theory

Caulfield, Erin

关键词: Expansions of the real field;    Complex subgroups;    Model theory;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/101541/CAULFIELD-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 】

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.