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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.
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By Ludwig-Maximilians-Universität München
5
11 ratings
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.
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