The wiki page about 'Determinacy' contains the following fragment:
"For every integer n, ZFC\P proves determinacy in the nth level of the difference hierarchy of $\Pi_3^0$ sets (...)"
(Here P stands for the powerset axiom.)
No specific references are given for this statement, but it is more or less suggested it might be found either in Simpson's 'Subsystems of second order arithmetic' or in some Friedman 1971 paper. Other sources suggested this could be Friedman 1971, Higher set theory and mathematical practice, Ann Math Log 2, 325-357.
Now I've checked both references reasonably well (I thought), as well as some other 1971 papers by Friedman, but I haven't found anything of help. Where can I find detailed proofs of the above result? Or did I overlook something that was right under my nose?
This result is quite recent. Here is a reference: Antonio Montalbán, Richard A. Shore, The limits of determinacy in second-order arithmetic (2012)