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You searched for +publisher:"University of Notre Dame" +contributor:("Anand Pillay, Research Director"). Showing records 1 – 3 of 3 total matches.

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University of Notre Dame

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

Degree: Mathematics, 2017, University of Notre Dame

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.

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

APA (6th 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 (16th 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 (7th 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

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

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

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

APA (6th 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

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th 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.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th 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.

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

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

<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

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

APA (6th 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

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th 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.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th 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.

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

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

.