JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. ABSTRACT. For any class of functions $ from R into R, AD(a) is the assertion that in every two person game on integers one of the two players has a winning

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... egy in the class $. It is shown, in ZF + DC + V = L(R), that for any a of cardinality < 24( (i.e. any a which is a surjective image of R) AD( t) implies AD (the Axiom of Determinacy).