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Miami University

1. Craft, Colin N. On Morley's Categoricity Theorem with an Eye Toward Forking.

Degree: MA, Mathematics, 2011, Miami University

URL: http://rave.ohiolink.edu/etdc/view?acc_num=miami1323475348

The primary result of this paper is Morley's
Categoricity Theorem that a complete theory T which is
¿-catecorigal for some uncountable cardinal ¿ is ¿-categorical for
every uncountable cardinal ¿. We prove this by proving a
characterization of uncountably categorical theories due to Baldwin
and Lachlan. Before the actual statement and proof of Morley's
theorem, we give an overview of the prerequisites from mathematical
logic needed to understand the theorem and its proof. After proving
Morley's theorem we briefly indicate some possible directions of
further study having to do with forking and the related notion of
independence of types.
*Advisors/Committee Members: Larson, Paul (Advisor).*

Subjects/Keywords: Mathematics; model theory; Morley's Categoricity Theorem; forking

Record Details Similar Records

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

APA (6^{th} Edition):

Craft, C. N. (2011). On Morley's Categoricity Theorem with an Eye Toward Forking. (Masters Thesis). Miami University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=miami1323475348

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

Craft, Colin N. “On Morley's Categoricity Theorem with an Eye Toward Forking.” 2011. Masters Thesis, Miami University. Accessed August 08, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=miami1323475348.

MLA Handbook (7^{th} Edition):

Craft, Colin N. “On Morley's Categoricity Theorem with an Eye Toward Forking.” 2011. Web. 08 Aug 2020.

Vancouver:

Craft CN. On Morley's Categoricity Theorem with an Eye Toward Forking. [Internet] [Masters thesis]. Miami University; 2011. [cited 2020 Aug 08]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=miami1323475348.

Council of Science Editors:

Craft CN. On Morley's Categoricity Theorem with an Eye Toward Forking. [Masters Thesis]. Miami University; 2011. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=miami1323475348

Miami University

2. Cotton, Michael R. Determinacy in the Low Levels of the Projective Hierarchy.

Degree: MA, Mathematics, 2012, Miami University

URL: http://rave.ohiolink.edu/etdc/view?acc_num=miami1343245802

We give an expository introduction to determinacy for
sets of reals. If we are to assume the Axiom of Choice, then not
all sets of reals can be determined. So we instead establish
determinacy for sets according to their levels in the usual
hierarchies of complexity. At a certain point ZFC is no longer
strong enough, and we must begin to assume large cardinals. The
primary results of this paper are Martin's theorems that Borel sets
are determined, homogeneously Suslin sets are determined, and if a
measurable cardinal ¿ exists then the complements of analytic sets
are ¿-homogeneously Suslin. We provide the necessary preliminaries,
prove Borel determinacy, introduce measurable cardinals and
ultrapowers, and then prove analytic determinacy from the existence
of a measurable cardinal. Finally, we give a very brief overview of
some further results which provide higher levels of determinacy
relative to larger cardinals.
*Advisors/Committee Members: Larson, Paul B. (Advisor).*

Subjects/Keywords: Logic; Mathematics; determinacy; descriptive set theory; large cardinal; measurable cardinal; set theory; projective; Borel; ZFC; homogeneously Suslin; ultrapower; Ramsey cardinal; analytic determinacy; analytic; Borel hierarchy; projective hierarchy; sets; Borel determinacy

Record Details Similar Records

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

APA (6^{th} Edition):

Cotton, M. R. (2012). Determinacy in the Low Levels of the Projective Hierarchy. (Masters Thesis). Miami University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=miami1343245802

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

Cotton, Michael R. “Determinacy in the Low Levels of the Projective Hierarchy.” 2012. Masters Thesis, Miami University. Accessed August 08, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=miami1343245802.

MLA Handbook (7^{th} Edition):

Cotton, Michael R. “Determinacy in the Low Levels of the Projective Hierarchy.” 2012. Web. 08 Aug 2020.

Vancouver:

Cotton MR. Determinacy in the Low Levels of the Projective Hierarchy. [Internet] [Masters thesis]. Miami University; 2012. [cited 2020 Aug 08]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=miami1343245802.

Council of Science Editors:

Cotton MR. Determinacy in the Low Levels of the Projective Hierarchy. [Masters Thesis]. Miami University; 2012. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=miami1343245802