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Weak Rudin–Keisler reductions on projective ideals

Volume 232 / 2016

Konstantinos A. Beros Fundamenta Mathematicae 232 (2016), 65-78 MSC: 03E15, 03E60, 03E05, 28A05. DOI: 10.4064/fm232-1-5


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.


  • Konstantinos A. BerosDepartment of Mathematics
    University of North Texas
    General Academics Building 435
    1155 Union Circle, #311430
    Denton, TX 76203-5017, U.S.A.

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