Dissertations, Theses, and Capstone Projects
Date of Degree
6-2020
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
Diophantine Problem, bi-interpretability, first-order logic, metabelian groups, Baumslag-Solitar group, wreath products, free monoid
Abstract
We first show that arithmetic is bi-interpretable (with parameters) with the free monoid and with partially commutative monoids with trivial center. This bi-interpretability implies that these monoids have the QFA property and that finitely generated submonoids of these monoids are definable. Moreover, we show that any recursively enumerable language in a finite alphabet X with two or more generators is definable in the free monoid. We also show that for metabelian Baumslag-Solitar groups and for a family of metabelian restricted wreath products, the Diophantine Problem is decidable. That is, we provide an algorithm that decides whether or not a given system of equations in these groups has a solution.
Recommended Citation
Lopez Cruz, Laura M., "Model Theory of Groups and Monoids" (2020). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/3685