In a recent article by Friedman, Gitman, and Kanovei, it was shown that AC does not imply DC in the context of second-order arithmetic. The proof was based on a constrution of a certain symmetric extension of L, using Jensen's Diamond Principle. In our talk, we will show that by modifying their construction, we can obtain a model of ZF in which, for a given n, Pi^1_n-determinacy holds, but Pi^1_k dependent choice for real numbers fails for some explicitly given value of k.
This presentation is based on joint work with Sandra Müller.