On special partitions of Dedekind- and Russell-sets

@article{Herrlich2012,
abstract = {A Russell set is a set which can be written as the union of a countable pairwise disjoint set of pairs no infinite subset of which has a choice function and a Russell cardinal is the cardinal number of a Russell set. We show that if a Russell cardinal $a$ has a ternary partition (see Section 1, Definition 2) then the Russell cardinal $a+2$ fails to have such a partition. In fact, we prove that if a ZF-model contains a Russell set, then it contains Russell sets with ternary partitions as well as Russell sets without ternary partitions. We then consider generalizations of this result.},
author = {Herrlich, Horst, Howard, Paul, Tachtsis, Eleftherios},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Axiom of Choice; Dedekind sets; Russell sets; generalizations of Russell sets; odd sized partitions; permutation models; Dedekind set; Russell set; odd sized partition; permutation models},
language = {eng},
number = {1},
pages = {105-122},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On special partitions of Dedekind- and Russell-sets},
url = {http://eudml.org/doc/246614},
volume = {53},
year = {2012},
}

TY - JOUR
AU - Herrlich, Horst
AU - Howard, Paul
AU - Tachtsis, Eleftherios
TI - On special partitions of Dedekind- and Russell-sets
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2012
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 53
IS - 1
SP - 105
EP - 122
AB - A Russell set is a set which can be written as the union of a countable pairwise disjoint set of pairs no infinite subset of which has a choice function and a Russell cardinal is the cardinal number of a Russell set. We show that if a Russell cardinal $a$ has a ternary partition (see Section 1, Definition 2) then the Russell cardinal $a+2$ fails to have such a partition. In fact, we prove that if a ZF-model contains a Russell set, then it contains Russell sets with ternary partitions as well as Russell sets without ternary partitions. We then consider generalizations of this result.
LA - eng
KW - Axiom of Choice; Dedekind sets; Russell sets; generalizations of Russell sets; odd sized partitions; permutation models; Dedekind set; Russell set; odd sized partition; permutation models
UR - http://eudml.org/doc/246614
ER -