Award Date

12-1-2020

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematical Sciences

First Committee Member

Derrick DuBose

Second Committee Member

Peter Shiue

Third Committee Member

Douglas Burke

Fourth Committee Member

Pushkin Kachroo

Number of Pages

124

Abstract

This thesis will be primarily focused on directly proving that the determinacy of Borel games in X^ω is equivalent to the determinacy of certain long open games, from a fragment of ZFC that’s well-known to be insufficient to prove Borel determinacy. The main theorem is a level by level result which shows the equivalence between determinacy of open games in a long tree, [Υ^α], and determinacy of Σ_0^α games in X^ω. In Chapter 9, we mimic the proof used in our main theorem to show that the determinacy of clopen games in the product space X^ω × ω^ω is equivalent to Borel determinacy in X^ω. In particular, the determinacy of clopen games from ω^(ω+ω) is equivalent to Borel determinacy in ω^ω.

Keywords

Borel games; Determinacy; Set theory

Disciplines

Mathematics

File Format

pdf

File Size

944 KB

Degree Grantor

University of Nevada, Las Vegas

Language

English

Rights

IN COPYRIGHT. For more information about this rights statement, please visit http://rightsstatements.org/vocab/InC/1.0/

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Mathematics Commons

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