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Authors:Sy D. Friedman   W. Hugh Woodin
Affiliation:Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 ; Department of Mathematics, University of California, Berkeley, California 94720
Abstract:We show that the supremum of the lengths of ${underset {sim }{Delta }}^1_2 $ prewellorderings of the reals can be $omega _{2}$, with $omega _{1}$ inaccessible to reals, assuming only the consistency of an inaccessible.

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