Home » Uncategorized » Determinacy of Borel games I

Determinacy of Borel games I

Gowers's Weblog

I’m trying to understand the famous result of Donald Martin that Borel games are determined, and by that I mean not just understand the proof line by line, but also understand why the lines are as they are. I have found some nice presentations online, in particular these notes by Shehzad Ahmed and this Masters thesis by Ross Bryant, which have been very helpful, not just in presenting the proofs line by line but also, to some extent, in doing things like explaining certain definitions that would otherwise seem a little strange. (Ahmed’s notes are good for a quick overview and Bryant’s thesis is good if you want full details.) Nevertheless, I think one can go further in that direction and speculate about how Martin came up with his proof. I’m actually talking not about his original 1975 proof but about a simpler argument he discovered about ten years…

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