Master of Science (MS)
First Committee Member
Second Committee Member
Third Committee Member
Fourth Committee Member
Number of Pages
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.
Borel games; Determinacy; Set theory
University of Nevada, Las Vegas
Yost, Katherine Aimee, "Equivalences of Determinacy Between Levels of the Borel Hierarchy and Long Games, and Some Generalizations" (2020). UNLV Theses, Dissertations, Professional Papers, and Capstones. 4094.
IN COPYRIGHT. For more information about this rights statement, please visit http://rightsstatements.org/vocab/InC/1.0/