Weak Rudin–Keisler reductions on projective ideals
Volume 232 / 2016
Fundamenta Mathematicae 232 (2016), 65-78
MSC: 03E15, 03E60, 03E05, 28A05.
DOI: 10.4064/fm232-1-5
Abstract
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.
