Logo Logo
Hilfe
Kontakt
Switch language to English
Some Axioms of Weak Determinacy
Some Axioms of Weak Determinacy
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.
determinacy, large cardinals, perfect sets
Kovachev, Bogomil
2009
Englisch
Universitätsbibliothek der Ludwig-Maximilians-Universität München
Kovachev, Bogomil (2009): Some Axioms of Weak Determinacy. Dissertation, LMU München: Fakultät für Mathematik, Informatik und Statistik
[thumbnail of Kovachev_Bogomil.pdf]
Vorschau
PDF
Kovachev_Bogomil.pdf

327kB

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.