Equivalence of partition properties and determinacy.
It is shown that, within L(R), the smallest inner model of set theory containing the reals, the axiom of determinacy is equivalent to the existence of arbitrarily large cardinals below Theta with the strong partition property kappa --> (kappa)(kappa).
Kechris
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Department of Mathematics, California Institute of Technology, Pasadena, California 91125.
Woodin
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WH