Some Axioms of Weak Determinacy

Kovachev, Bogomil (2009): Some Axioms of Weak Determinacy. Dissertation, LMU München: Faculty of Mathematics, Computer Science and Statistics

Abstract

We consider two-player games of perfect information of length some cardinal $\kappa$. It is well-known that for $\kappa \geq \omega_1$ the full axiom of determinacy for these games fails, thus we investigate three weaker forms of it. We obtain the measurability of $\kappa^{+}$ under $DC_{\kappa}$-the axiom of dependent choices generalized to $\kappa$. We generalize the notions of perfect and meager sets and provide characterizations with some special kinds of games. We show that under an additional assumption one of our three axioms follows from the other two.

• Item Type: Theses (Dissertation, LMU Munich)
• Keywords: determinacy, large cardinals, perfect sets
• Subjects: 500 Natural sciences and mathematics > 510 Mathematics; 500 Natural sciences and mathematics
• Faculties: Faculty of Mathematics, Computer Science and Statistics
• Language: English
• Date of oral examination: 16. October 2009
• 1. Referee: Donder, Hans-Dieter
• Signature of the printed copy: 0001/UMC 18225