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Could someone point me toward a proof that "ZF + AD + every set of reals is Suslin" (+ $\mathsf{DC}\_\mathbb{R}$?) implies $\mathsf{AD}\_\mathbb{R}$, either with a reference or a hint?

I am interested how local the proof is; that is, which sets of reals need to be Suslin in order to show the determinacy of a particular real game.

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  • $\begingroup$ Sorry about the formatting. I cannot seem to get a subscript \mathbb{R} in the body of the question. $\endgroup$
    – Trevor Wilson
    Commented Oct 17, 2012 at 16:36
  • $\begingroup$ Hi Trevor. Isn't this covered in Richard's paper (More structural consequences of AD)? $\endgroup$
    – Andrés E. Caicedo
    Commented Oct 17, 2012 at 16:43
  • $\begingroup$ Hi Andres, it looks like he just says it is due independently to Martin and Woodin, and is unpublished. $\endgroup$
    – Trevor Wilson
    Commented Oct 17, 2012 at 16:57
  • $\begingroup$ I might be mistaken but if I remember correctly, I saw something like this result in the Cabal reprints (in Steve's Article, volume I). If you don't have them, I'll try to check if it's indeed there later. $\endgroup$
    – Rachid Atmai
    Commented Oct 17, 2012 at 20:03
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    $\begingroup$ You can find it here : users.miamioh.edu/larsonpb/adplusbook_public.pdf $\endgroup$
    – Paul Larson
    Commented Jul 27, 2018 at 5:42

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