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・ Axle counter
・ Axle hitch
・ Axiom of countable choice
・ Axiom of dependent choice
・ Axiom of determinacy
・ Axiom of empty set
・ Axiom of Equity
・ Axiom of extensionality
・ Axiom of global choice
・ Axiom of infinity
・ Axiom of limitation of size
・ Axiom of Maria
・ Axiom of pairing
・ Axiom of power set
・ Axiom of projective determinacy
Axiom of real determinacy
・ Axiom of reducibility
・ Axiom of regularity
・ Axiom of union
・ Axiom S5
・ Axiom schema
・ Axiom schema of predicative separation
・ Axiom schema of replacement
・ Axiom schema of specification
・ Axiom Telecom
・ Axiom Verge
・ Axiom-man
・ Axioma
・ Axioma Ethica Odini
・ Axiomatic (album)


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Axiom of real determinacy : ウィキペディア英語版
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.
ADR is equivalent to AD plus the axiom of uniformization.



抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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