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You searched for +publisher:"Miami University" +contributor:("Larson, Paul"). Showing records 1 – 2 of 2 total matches.

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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

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

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

APA (6th 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 (16th 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 (7th 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

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

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

APA (6th 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 (16th 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 (7th 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

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