Some Axioms of Weak Determinacy

Kovachev, Bogomil (2009): Some Axioms of Weak Determinacy. Dissertation, LMU München: Fakultät für Mathematik, Informatik und Statistik

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.

• Dokumententyp: Dissertationen (Dissertation, LMU München)
• Keywords: determinacy, large cardinals, perfect sets
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik ; 500 Naturwissenschaften und Mathematik
• Fakultäten: Fakultät für Mathematik, Informatik und Statistik
• Sprache der Hochschulschrift: Englisch
• Datum der mündlichen Prüfung: 16. Oktober 2009
• 1. Bericht­erstatter:in: Donder, Hans-Dieter