Some Model Theory of Free Groups

<p>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.</p> <p>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).</p>

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics

Grantor

The Graduate School and University Center of The City University of New York

Year dc:date.available

2021

Author dc:creator

• Natoli, Christopher James

Advisor dc:contributor.advisor

• Olga Kharlampovich

Committee members dc:contributor.committeemember

• Ilya Kapovich
• Vladimir Shpilrain

• Algebra
• Logic and Foundations
• group theory
• model theory
• free groups

Repository record dc:identifier

https://academicworks.cuny.edu/gc_etds/4132

OAI identifier oai:identifier

oai:academicworks.cuny.edu:gc_etds-5192