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Full-Text Articles in Physical Sciences and Mathematics
Some Model Theory Of Free Groups, Christopher James Natoli
Some Model Theory Of Free Groups, Christopher James Natoli
Dissertations, Theses, and Capstone Projects
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 …
Interstructure Lattices And Types Of Peano Arithmetic, Athar Abdul-Quader
Interstructure Lattices And Types Of Peano Arithmetic, Athar Abdul-Quader
Dissertations, Theses, and Capstone Projects
The collection of elementary substructures of a model of PA forms a lattice, and is referred to as the substructure lattice of the model. In this thesis, we study substructure and interstructure lattices of models of PA. We apply techniques used in studying these lattices to other problems in the model theory of PA.
In Chapter 2, we study a problem that had its origin in Simpson, who used arithmetic forcing to show that every countable model of PA has an expansion to PA∗ that is pointwise definable. Enayat later showed that there are 2ℵ0 models with …