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You searched for +publisher:"University of Notre Dame" +contributor:("Cameron Hill, Committee Member"). Showing records 1 – 3 of 3 total matches.

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University of Notre Dame

1. Donald A Brower. Aspects of stability in simple theories</h1>.

Degree: Mathematics, 2012, University of Notre Dame

Simple theories are a strict extension of stable theories for which non-forking independence is a nice independence relation. However, not much is known about how the simple unstable theories differ from the strictly stable ones. This work looks at three aspects of simple theories and uses them to give a better picture of the differences between the two classes. First, we look at the property of weakly eliminating hyperimaginaries and show that it is equivalent to forking and thorn-forking independence coinciding. Second, we look at the stable forking conjecture}, a strong statement asserting that simple unstable theories have an essentially stable “core,” and prove that it holds between elements having SU-rank 2 and finite SU-rank. Third, we consider a property on indiscernible sequences that is known to hold in every stable theory, and show it holds on, at most, a subset of simple theories out of all possible first order theories. Advisors/Committee Members: Cameron Hill, Committee Member, Steven Buechler, Committee Chair, Julia Knight, Committee Member, Sergei Starchenko, Committee Member.

Subjects/Keywords: indiscernible sequence; classification theory; model theory; hyperimaginary; Logic

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

APA (6th Edition):

Brower, D. A. (2012). Aspects of stability in simple theories</h1>. (Thesis). University of Notre Dame. Retrieved from https://curate.nd.edu/show/9306sx63f5x

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):

Brower, Donald A. “Aspects of stability in simple theories</h1>.” 2012. Thesis, University of Notre Dame. Accessed December 05, 2020. https://curate.nd.edu/show/9306sx63f5x.

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

MLA Handbook (7th Edition):

Brower, Donald A. “Aspects of stability in simple theories</h1>.” 2012. Web. 05 Dec 2020.

Vancouver:

Brower DA. Aspects of stability in simple theories</h1>. [Internet] [Thesis]. University of Notre Dame; 2012. [cited 2020 Dec 05]. Available from: https://curate.nd.edu/show/9306sx63f5x.

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

Council of Science Editors:

Brower DA. Aspects of stability in simple theories</h1>. [Thesis]. University of Notre Dame; 2012. Available from: https://curate.nd.edu/show/9306sx63f5x

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


University of Notre Dame

2. Jesse Werth Johnson. Computable Model Theory for Uncountable Structures</h1>.

Degree: Mathematics, 2013, University of Notre Dame

Using classical definitions from admissible set theory, we examine computable model theory for uncountable structures. We begin the first chapter by recalling several classic results from α-recursion, as stated in Greenberg and Knight. We give a few examples of “ω2-computable” structures. In the second chapter, we continue work of Greenberg and Knight on “ω2-computable” structure theory. All results in this chapter are joint with Jacob Carson, Julia Knight, Karen Lange, Charles McCoy, and John Wallbaum. We define the arithmetical hierarchy through all countable levels (not just finite levels). The definition resembles that of the hyperarithmetical hierarchy. We obtain analogues of the results of Chisholm and Ash, Knight, Manasse, and Slaman, saying that a relation is relatively intrinsically Σ0α if and only if it is definable by a computable Σα formula. In the third chapter, we focus on quasiminimal-excellent classes, which are important classes of structures in modern model theory. We give a definition for κ+-computable categoricity and give properties of classes of structures, under which the unique element of size κ+ has a κ+-computable copy and is κ+02-categorical. We then show that any class satisfying these properties is κ+-computably categorical if and only if there is no triple (N’,N,M) of structures of dimension κ such that MNN’ and M is “closed” in N and N’, but N is not “closed” in N’. We then apply this result to some well-known examples of quasiminimal-excellent classes, showing that the pseudo-exponential field of size κ+ is not κ+-computably categorical, but the “Zil'ber cover” is relatively κ+-computably categorical. We end by connecting the results of computable categoricity to axiomatizability for quasiminimal-excellent classes. Advisors/Committee Members: Sergei Starchenko, Committee Member, Cameron Hill, Committee Member, Julia Knight, Committee Member, John Baldwin, Committee Member.

Subjects/Keywords: recursive structure; computable categoricity; quasiminimal excellent; computable structure; uncountable structure

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

APA (6th Edition):

Johnson, J. W. (2013). Computable Model Theory for Uncountable Structures</h1>. (Thesis). University of Notre Dame. Retrieved from https://curate.nd.edu/show/ns064457k8r

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):

Johnson, Jesse Werth. “Computable Model Theory for Uncountable Structures</h1>.” 2013. Thesis, University of Notre Dame. Accessed December 05, 2020. https://curate.nd.edu/show/ns064457k8r.

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

MLA Handbook (7th Edition):

Johnson, Jesse Werth. “Computable Model Theory for Uncountable Structures</h1>.” 2013. Web. 05 Dec 2020.

Vancouver:

Johnson JW. Computable Model Theory for Uncountable Structures</h1>. [Internet] [Thesis]. University of Notre Dame; 2013. [cited 2020 Dec 05]. Available from: https://curate.nd.edu/show/ns064457k8r.

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

Council of Science Editors:

Johnson JW. Computable Model Theory for Uncountable Structures</h1>. [Thesis]. University of Notre Dame; 2013. Available from: https://curate.nd.edu/show/ns064457k8r

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


University of Notre Dame

3. Steven M. VanDenDriessche. Embedding Computable Infinitary Equivalence nto P-Groups</h1>.

Degree: Mathematics, 2013, University of Notre Dame

We examine the relation between the uniformity of a collection of operators witnessingTuring computable embeddings, and the existence of an operator witnessingthe universality of a class. The primary equivalence relation studied here is computableinfinitary Σα equivalence. This project of exploiting uniformity of Turingcomputable embeddings to construct a limit embedding is carried out entirely in thecontext of countable reduced abelian p-groups. One may look at this program as eithera project in the computable structure theory of abelian p-groups, or as a projectin the construction of limits of sequences of uniform Turing computable operators. In an attempt to explore the boundary between computable infinitary Σα equivalenceand isomorphism, we show that for any computable , certain classes of countablereduced abelian p-groups are universal for ∼cα under Turing computable embedding.Further, the operators witnessing these embeddings are extremely uniform. Exploiting the uniformity of the embeddings, we produce operators which are,in some sense, limits of the embeddings witnessing the universality of the classesof countable reduced abelian p-groups. This is approached in three dierent ways:transnite recursion on ordinal notation, Barwise-Kreisel Compactness, and hyperarithemeticalsaturation. Finally, we work in admissible set theory, and use BarwiseCompactness and ΣA-saturation to generalize selected results. Advisors/Committee Members: Russell G. Miller, Committee Member, Julia F. Knight, Committee Chair, Cameron Hill, Committee Member, Sergei Starchenko, Committee Member.

Subjects/Keywords: computable structure theory; abelian groups

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

APA (6th Edition):

VanDenDriessche, S. M. (2013). Embedding Computable Infinitary Equivalence nto P-Groups</h1>. (Thesis). University of Notre Dame. Retrieved from https://curate.nd.edu/show/9z902z12x9k

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):

VanDenDriessche, Steven M.. “Embedding Computable Infinitary Equivalence nto P-Groups</h1>.” 2013. Thesis, University of Notre Dame. Accessed December 05, 2020. https://curate.nd.edu/show/9z902z12x9k.

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

MLA Handbook (7th Edition):

VanDenDriessche, Steven M.. “Embedding Computable Infinitary Equivalence nto P-Groups</h1>.” 2013. Web. 05 Dec 2020.

Vancouver:

VanDenDriessche SM. Embedding Computable Infinitary Equivalence nto P-Groups</h1>. [Internet] [Thesis]. University of Notre Dame; 2013. [cited 2020 Dec 05]. Available from: https://curate.nd.edu/show/9z902z12x9k.

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

Council of Science Editors:

VanDenDriessche SM. Embedding Computable Infinitary Equivalence nto P-Groups</h1>. [Thesis]. University of Notre Dame; 2013. Available from: https://curate.nd.edu/show/9z902z12x9k

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

.