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Statements

Subject Item
dbr:Partition_cardinal
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dbr:Strong_partition_cardinal
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Strong partition cardinal
rdfs:comment
In Zermelo–Fraenkel set theory without the axiom of choice a strong partition cardinal is an uncountable well-ordered cardinal such that every partition of the set of size subsets of into less than pieces has a homogeneous set of size . The existence of strong partition cardinals contradicts the axiom of choice. The Axiom of determinacy implies that ℵ1 is a strong partition cardinal.
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1123353784
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dbr:Well-ordered dbr:Axiom_of_determinacy dbr:Homogeneous_(large_cardinal_property) dbr:Uncountable dbr:Partition_(set_theory) dbc:Cardinal_numbers dbr:Zermelo–Fraenkel_set_theory dbr:Transactions_of_the_American_Mathematical_Society dbr:Cardinality dbr:Journal_of_Symbolic_Logic dbr:Axiom_of_choice
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In Zermelo–Fraenkel set theory without the axiom of choice a strong partition cardinal is an uncountable well-ordered cardinal such that every partition of the set of size subsets of into less than pieces has a homogeneous set of size . The existence of strong partition cardinals contradicts the axiom of choice. The Axiom of determinacy implies that ℵ1 is a strong partition cardinal.
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wikipedia-en:Strong_partition_cardinal?oldid=1123353784&ns=0
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wikipedia-en:Strong_partition_cardinal
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wikipedia-en:Strong_partition_cardinal
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