2
$\begingroup$

Looking for a subject to develop an undergraduate search project, I found the concept of Determinacy, a subfield of set theory that examines the conditions under which one player of a game has a winning strategy, as Wikipedia states. I've read just a little bit about it, so I'd like to get an introductory book to learn the concept and explore suitable applications. I'm a beginner in set theory and game theory and I'd be grateful with some indications and suggestions.

As far, I got Thomas Jech's Set Theory. In it, Determinacy is the name of chapter $33$. Since it doesn't present a diagram of interdependence between the chapters, I don't know if it'd be a good idea (the chapter $33$ starts at page $627$). Hrbacek and Jech's Introduction to set theory discusses it too, but I'd like to appeal to your opinion and maybe to find some better.

In short, let's say I'm interesting in a book by which it I could learn about Determinacy and find a nice application, like the proof of the determinacy in some class of games... Thanks in advance!

$\endgroup$
2
$\begingroup$

I think descriptive set theory books are the way to go; either Kechris or Moschovakis will serve you well.

Personally, for a first introduction I vastly prefer Kechris; specifically, I would read the beginning few chapters to get a good sense of the context (Polish spaces, Borel sets, some tree combinatorics) and then would read chapters 20-21, diving back to the earlier chapters when needed.

Chapter 6 ("The playful universe") of Moschovakis goes into more sophisticated material, but is also much heavier.

$\endgroup$
1
  • $\begingroup$ I think that Kechris's book is heavier, but I don't remember holding both of them for comparison. $\endgroup$
    – Asaf Karagila
    Aug 9 '17 at 21:00

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.