Dissertations, Theses, and Capstone Projects
Date of Degree
2-2021
Document Type
Dissertation
Degree Name
Ph.D.
Program
Mathematics
Advisor
Olga Kharlampovich
Committee Members
Ilya Kapovich
Vladimir Shpilrain
Subject Categories
Algebra | Logic and Foundations
Keywords
group theory, model theory, free groups
Abstract
There are two main sets of results, both pertaining to the model theory of free groups. In the first set of results, we prove that non-abelian free groups of finite rank at least 3 or of countable rank are not A-homogeneous. We then build on the proof of this result to show that two classes of groups, namely finitely generated free groups and finitely generated elementary free groups, fail to form A-Fraisse classes and that the class of non-abelian limit groups fails to form a strong A-Fraisse class.
The second main result is that if a countable group is elementarily equivalent to a non-abelian free group and all of its finitely generated abelian subgroups are cyclic, then the group is a union of a chain of regular NTQ groups (i.e., hyperbolic towers).
Recommended Citation
Natoli, Christopher James, "Some Model Theory of Free Groups" (2021). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/4132