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University of Notre Dame

1. Paul Anh McEldowney. Model-Theoretic Galois Cohomology</h1>.

Degree: Mathematics, 2017, University of Notre Dame

URL: https://curate.nd.edu/show/b5644q8065d

This thesis provides a self-contained and
thorough exposition of Proposition 3.3 of Pillay’s 1997 paper “Some
Remarks on Galois Cohomology and Definability.” As such, this
thesis includes all of the necessary background definitions,
results, and proofs required to understand this
proposition.
*Advisors/Committee Members: Curtis Franks, Research Director, Sergei Starchkenko, Committee Member, Julia Knight, Committee Member, Anand Pillay, Research Director.*

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

McEldowney, P. A. (2017). Model-Theoretic Galois Cohomology</h1>. (Thesis). University of Notre Dame. Retrieved from https://curate.nd.edu/show/b5644q8065d

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

McEldowney, Paul Anh. “Model-Theoretic Galois Cohomology</h1>.” 2017. Thesis, University of Notre Dame. Accessed July 07, 2020. https://curate.nd.edu/show/b5644q8065d.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

McEldowney, Paul Anh. “Model-Theoretic Galois Cohomology</h1>.” 2017. Web. 07 Jul 2020.

Vancouver:

McEldowney PA. Model-Theoretic Galois Cohomology</h1>. [Internet] [Thesis]. University of Notre Dame; 2017. [cited 2020 Jul 07]. Available from: https://curate.nd.edu/show/b5644q8065d.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

McEldowney PA. Model-Theoretic Galois Cohomology</h1>. [Thesis]. University of Notre Dame; 2017. Available from: https://curate.nd.edu/show/b5644q8065d

Not specified: Masters Thesis or Doctoral Dissertation

University of Notre Dame

2. Somayeh Vojdani. On Presburger Arithmetic, Nonstandard Finite Cyclic Groups, and Definable Compactifications</h1>.

Degree: Mathematics, 2016, University of Notre Dame

URL: https://curate.nd.edu/show/k3569309463

It is known that any model of the theory of
the group of integers can be decomposed into a direct sum of a
torsion-free divisible abelian group and an elementary substructure
of the profinite group. We give a similar result for models of the
theory of Presburger arithmetic and discuss orderings on direct
summands. We show that the torsion-free divisible abelian group is
densely ordered and we find the number of non-isomorphic expansions
of the profinite group to a model of Presburger arithmetic. We also
give a description of the f-generic types of saturated models of
Presburger arithmetic. We consider nonstandard
analogues of finite cyclic groups as a family of groups defined in
an elementary extension of Presburger arithmetic. Since the theory
of Presburger arithmetic has NIP, any such group H has a smallest
type-definable subgroup of bounded index. Each quotient is a
compact group under the logic topology. The main result of this
thesis is the classification of these compact
groups. The universal definable compactification
of a group G, in a language in which all the subsets of G are
definable, coincides with the Bohr compactification bG of G
considered as a discrete group. For an abelian group G, in
particular the group of integers, we compute the type-connected
component. We show that adding predicates for certain subsets of G
is enough to get bG as the universal
compactification.
*Advisors/Committee Members: Philipp Hieronymi, Committee Member, Peter Cholak, Committee Member, Gabriel Conant, Committee Member, Anand Pillay, Research Director.*

Subjects/Keywords: Model theory

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Vojdani, S. (2016). On Presburger Arithmetic, Nonstandard Finite Cyclic Groups, and Definable Compactifications</h1>. (Thesis). University of Notre Dame. Retrieved from https://curate.nd.edu/show/k3569309463

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Vojdani, Somayeh. “On Presburger Arithmetic, Nonstandard Finite Cyclic Groups, and Definable Compactifications</h1>.” 2016. Thesis, University of Notre Dame. Accessed July 07, 2020. https://curate.nd.edu/show/k3569309463.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Vojdani, Somayeh. “On Presburger Arithmetic, Nonstandard Finite Cyclic Groups, and Definable Compactifications</h1>.” 2016. Web. 07 Jul 2020.

Vancouver:

Vojdani S. On Presburger Arithmetic, Nonstandard Finite Cyclic Groups, and Definable Compactifications</h1>. [Internet] [Thesis]. University of Notre Dame; 2016. [cited 2020 Jul 07]. Available from: https://curate.nd.edu/show/k3569309463.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Vojdani S. On Presburger Arithmetic, Nonstandard Finite Cyclic Groups, and Definable Compactifications</h1>. [Thesis]. University of Notre Dame; 2016. Available from: https://curate.nd.edu/show/k3569309463

Not specified: Masters Thesis or Doctoral Dissertation

University of Notre Dame

3. Gregory Cousins. Some Model Theory of Fields and Differential Fields</h1>.

Degree: Mathematics, 2019, University of Notre Dame

URL: https://curate.nd.edu/show/k3569310027

<span>In this dissertation, we attempt
to study connections between various properties of fields, namely
boundedness, largeness, and strong form of model completeness
called “almost quantifier elimination”. The first chapter consists
of background information, and the second chapter is more or less
devoted to the study of fields in the ring language, possible
expanded by constants. We show that large, perfect fields with
almost quantifier elimination are geometric and fail to have a
strong notion of
unboundedness.</span> <span>The third
chapter is dedicated to the study, and characterization, of
differential fields with a notion of largeness for
differential-algebraic sets. We also make some brief comments on
notions of largeness for fields equipped with an
automorphism.</span> The fourth chapter is
based on joint work with Quentin Brouette, Anand Pillay, and
Françoise Point in which we prove that if T is a theory of large,
bounded fields of characteristic 0 with almost quantifier
elimination, and T’ is the model companion of T together with the
statement “d is a derivation” then for any model
(U, d) of T’, differential subfield K of U such that C(K) is a
model of T, and logarithmic differential equation dlog(z)=a
(defined over some algebraic group G that is definable over C(K)),
there is a strongly normal extension L of K for the equation with L
a differential subfield of U.
*Advisors/Committee Members: Julia Knight, Committee Member, Sergei Starchenko, Committee Member, Anand Pillay, Research Director, Peter Cholak, Committee Member, James Freitag, Committee Member.*

Subjects/Keywords: field theory; differential algebra; logic; model theory

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Cousins, G. (2019). Some Model Theory of Fields and Differential Fields</h1>. (Thesis). University of Notre Dame. Retrieved from https://curate.nd.edu/show/k3569310027

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Cousins, Gregory. “Some Model Theory of Fields and Differential Fields</h1>.” 2019. Thesis, University of Notre Dame. Accessed July 07, 2020. https://curate.nd.edu/show/k3569310027.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Cousins, Gregory. “Some Model Theory of Fields and Differential Fields</h1>.” 2019. Web. 07 Jul 2020.

Vancouver:

Cousins G. Some Model Theory of Fields and Differential Fields</h1>. [Internet] [Thesis]. University of Notre Dame; 2019. [cited 2020 Jul 07]. Available from: https://curate.nd.edu/show/k3569310027.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Cousins G. Some Model Theory of Fields and Differential Fields</h1>. [Thesis]. University of Notre Dame; 2019. Available from: https://curate.nd.edu/show/k3569310027

Not specified: Masters Thesis or Doctoral Dissertation