I want to read the proof of projective determinacy. But every proof I could find (martin-steel original, koepke's, the proof in schindler's book, martin's new book) is too long. Are there a simple proof of PD? If there is no such one, then are there a guide line about the idea behind the proof?

  • $\begingroup$ Proof from what axioms? It is not provable in ZF(C). $\endgroup$
    – Wojowu
    Jun 24 at 9:47
  • $\begingroup$ of course in ZFC+there are n woodin cardinals for any n $\endgroup$ Jun 24 at 10:02
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    $\begingroup$ Often times the "exact consistency strength" is a bit harder to state, grasp, and work with. This is why so many of the proofs that require Woodin(s)+a sharp are done with Woodin(s)+measurable; and why the simpler proofs of things like generic absoluteness are from a supercompact rather than a proper class of Woodin cardinals. If you just want to understand the idea, I suggest you start by finding one of those simplified proofs, then start building your arsenal of tools (e.g. stationary tower and how it relates to generic absoluteness and determinacy proofs), and then go for the long proofs. $\endgroup$
    – Asaf Karagila
    Jun 24 at 10:34
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    $\begingroup$ I will also add that you're asking for a theorem that is a pinnacle of technical concepts. It's no wonder that the proofs are very long and complicated and have a lot of preliminary knowledge necessary. It's a long and technical subject. That's just how mathematics work, very often simple questions have very very very complicated answers. $\endgroup$
    – Asaf Karagila
    Jun 24 at 10:35
  • $\begingroup$ Itay's write ups are very clean, in my opinion. Take a look at his chapter in the Handbook. That said, it may help if you indicate what specific difficulties you have in mind. $\endgroup$ Jul 7 at 17:00

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