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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.
Konstantinos A. Beros. "Weak Rudin-Keisler reductions on projective ideals." Fundamenta Mathematicae 232.1 (2016): 65-78. <http://eudml.org/doc/283293>.
@article{KonstantinosA2016, 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 Π¹₁ equivalence relation. This proof enables us (under PD) to generalize Hjorth’s result to the classes of $Π¹_\{2n+1\}$ equivalence relations.}, author = {Konstantinos A. Beros}, journal = {Fundamenta Mathematicae}, language = {eng}, number = {1}, pages = {65-78}, title = {Weak Rudin-Keisler reductions on projective ideals}, url = {http://eudml.org/doc/283293}, volume = {232}, year = {2016}, }
TY - JOUR AU - Konstantinos A. Beros TI - Weak Rudin-Keisler reductions on projective ideals JO - Fundamenta Mathematicae PY - 2016 VL - 232 IS - 1 SP - 65 EP - 78 AB - 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 $Π¹_{2n+1}$ equivalence relations. LA - eng UR - http://eudml.org/doc/283293 ER -