Submitted. PDF. arXiv. Bibtex.
We describe a construction of a model of second order arithmetic in which boldface $\Pi^1_n$-determinacy holds, but lightface $\Pi^1_{n+2}$-DC fails, thus showing that no projective level of determinacy implies full $DC_{\mathbb{R}}$. The construction builds upon the work of Gitman, Friedman, and Kanovei.