Beros, Konstantinos A. Weak Rudin-Keisler reductions on projective ideals. (English) Zbl 1432.03085 Fundam. Math. 232, No. 1, 65-78 (2016). Summary: We consider a slightly modified form of the standard Rudin-Keisler order on ideals and demonstrate the existence of complete (with respect to this order) ideals in various projective classes. Using our methods, we obtain a simple proof of Hjorth’s theorem on the existence of a complete \(\mathbf \Pi ^1_1\) equivalence relation. This proof enables us (under PD) to generalize Hjorth’s result to the classes of \(\boldsymbol {\Pi}^1_{2n+1}\) equivalence relations. MSC: 03E15 Descriptive set theory 03E60 Determinacy principles 03E05 Other combinatorial set theory 28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets PDFBibTeX XMLCite \textit{K. A. Beros}, Fundam. Math. 232, No. 1, 65--78 (2016; Zbl 1432.03085) Full Text: DOI arXiv