Advanced search options

Sorted by: relevance · author · university · date | New search

You searched for `+publisher:"University of Notre Dame" +contributor:("Cameron Hill, Committee Member")`

.
Showing records 1 – 3 of
3 total matches.

▼ Search Limiters

University of Notre Dame

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

Degree: Mathematics, 2012, University of Notre Dame

URL: https://curate.nd.edu/show/9306sx63f5x

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

Record Details Similar Records

❌

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

APA (6^{th} 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 (16^{th} 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 (7^{th} 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

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

URL: https://curate.nd.edu/show/ns064457k8r

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
“ω_{2}-computable” structures.
In the second chapter, we continue work of Greenberg and
Knight on “ω_{2}-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
Σ^{0}_{α} if and only if it
is definable by a computable Σ_{α}
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^{+}-Δ^{0}_{2}-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 *M* ⊆
*N* ⊆ *N’* 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

Record Details Similar Records

❌

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

APA (6^{th} 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

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} 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.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} 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.

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

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

URL: https://curate.nd.edu/show/9z902z12x9k

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

Record Details Similar Records

❌

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

APA (6^{th} 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

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} 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.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} 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.

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

Not specified: Masters Thesis or Doctoral Dissertation