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Statements

Subject Item
dbr:Wadge_hierarchy
dbo:wikiPageWikiLink
dbr:Difference_hierarchy
Subject Item
dbr:Difference_hierarchy
rdf:type
yago:WikicatMathematicalLogicHierarchies yago:Hierarchy108377806 yago:Arrangement107938773 yago:Series108457976 yago:Ordering108456993 yago:Group100031264 yago:Abstraction100002137
rdfs:label
Difference hierarchy
rdfs:comment
In set theory, a branch of mathematics, the difference hierarchy over a pointclass is a hierarchy of larger pointclassesgenerated by taking differences of sets. If Γ is a pointclass, then the set of differences in Γ is . In usual notation, this set is denoted by 2-Γ. The next level of the hierarchy is denoted by 3-Γ and consists of differences of three sets:. This definition can be extended recursively into the transfinite to α-Γ for some ordinal α. In the Borel hierarchy, Felix Hausdorff and Kazimierz Kuratowski proved that the countable levels of the difference hierarchy over Π0γ giveΔ0γ+1.
dcterms:subject
dbc:Descriptive_set_theory dbc:Mathematical_logic_hierarchies
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dbr:Hierarchy_(mathematics) dbr:Pointclass dbr:Countable dbr:Complement_(set_theory) dbr:Set_theory dbr:Kazimierz_Kuratowski dbr:Transfinite_number dbr:Felix_Hausdorff dbr:Ordinal_number dbr:Borel_sets dbc:Mathematical_logic_hierarchies dbc:Descriptive_set_theory
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dbo:abstract
In set theory, a branch of mathematics, the difference hierarchy over a pointclass is a hierarchy of larger pointclassesgenerated by taking differences of sets. If Γ is a pointclass, then the set of differences in Γ is . In usual notation, this set is denoted by 2-Γ. The next level of the hierarchy is denoted by 3-Γ and consists of differences of three sets:. This definition can be extended recursively into the transfinite to α-Γ for some ordinal α. In the Borel hierarchy, Felix Hausdorff and Kazimierz Kuratowski proved that the countable levels of the difference hierarchy over Π0γ giveΔ0γ+1.
prov:wasDerivedFrom
wikipedia-en:Difference_hierarchy?oldid=958790728&ns=0
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2008
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wikipedia-en:Difference_hierarchy
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dbr:Hierarchy_(mathematics)
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dbr:Difference_hierarchy
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dbr:Difference_hierarchy