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

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Abstract
We consider twoplayer games of perfect information of length some cardinal $\kappa$. It is wellknown 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:  Thesis (Dissertation, LMU Munich) 

Keywords:  determinacy, large cardinals, perfect sets 
Subjects:  600 Natural sciences and mathematics > 510 Mathematics 600 Natural sciences and mathematics 
Faculties:  Faculty of Mathematics, Computer Science and Statistics 
Language:  English 
Date Accepted:  16. October 2009 
1. Referee:  Donder, HansDieter 
Persistent Identifier (URN):  urn:nbn:de:bvb:19109320 
MD5 Checksum of the PDFfile:  78b1cd5379cc837f2a42da2a29b4e7da 
Signature of the printed copy:  0001/UMC 18225 
ID Code:  10932 
Deposited On:  23. Dec 2009 13:45 
Last Modified:  16. Oct 2012 08:34 
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