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).
","abstract_html":"<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>","abstract_has_math":false,"creators":["Natoli, Christopher James"],"institution":"The Graduate School and University Center of The City University of New York","degree_name":"Doctor of Philosophy","degree_level":"Doctoral","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":["Olga Kharlampovich"],"committee_chairs":[],"committee_members":["Ilya Kapovich","Vladimir Shpilrain"],"year":2021,"date_issued":"2021-02-01T08:00:00Z","date_published":"2021-02-01T08:00:00Z","updated_at":"2026-07-24T01:58:49Z","subjects":["Algebra","Logic and Foundations","group theory","model theory","free groups"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://academicworks.cuny.edu/gc_etds/4132","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Olga Kharlampovich"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Ilya Kapovich","Vladimir Shpilrain"]},{"key":"dc:creator","label":"Author","values":["Natoli, Christopher James"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2020-12-09T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["The Graduate School and University Center of The City University of New York"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Algebra","Logic and Foundations","group theory","model theory","free groups"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://academicworks.cuny.edu/gc_etds/4132"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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).
"]},{"key":"dc:title","label":"Title","values":["Some Model Theory of Free Groups"]}]}],"canonical_facts":{"dc:contributor.advisor":["Olga Kharlampovich"],"dc:contributor.committeemember":["Ilya Kapovich","Vladimir Shpilrain"],"dc:creator":["Natoli, Christopher James"],"dc:date.available":["2020-12-09T08:00:00Z"],"dc:description.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).
"],"dc:identifier":["https://academicworks.cuny.edu/gc_etds/4132"],"dc:subject":["Algebra","Logic and Foundations","group theory","model theory","free groups"],"dc:title":["Some Model Theory of Free Groups"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Doctor of Philosophy"],"thesis:institution_name":["The Graduate School and University Center of The City University of New York"]},"updated_at":"2026-07-24T01:58:49Z"}