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Axiom of real determinacy
In mathematics, the axiom of real determinacy (abbreviated as ADR) is an axiom in set theory. It states the following:
Consider infinite two-person games with perfect information. Then, every game of length ω where both players choose real numbers is determined, i.e., one of the two players has a winning strategy.
The axiom of real determinacy is a stronger version of the axiom of determinacy, which makes the same statement about games where both players choose integers; it is inconsistent with the axiom of choice. ADR also implies the existence of inner models with certain large cardinals.
10-26-2009 08:16:03
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details