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 Π¹₁ equivalence relation. This proof enables us (under PD) to generalize Hjorth’s result to the classes of equivalence relations.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm232-1-5,
author = {Konstantinos A. Beros},
title = {Weak Rudin-Keisler reductions on projective ideals},
journal = {Fundamenta Mathematicae},
volume = {233},
year = {2016},
pages = {65-78},
zbl = {06497294},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm232-1-5}
}
Konstantinos A. Beros. Weak Rudin-Keisler reductions on projective ideals. Fundamenta Mathematicae, Tome 233 (2016) pp. 65-78. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm232-1-5/