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Statements

Subject Item
dbr:Homogeneous_tree
rdfs:label
Homogeneous tree
rdfs:comment
In descriptive set theory, a tree over a product set is said to be homogeneous if there is a system of measures such that the following conditions hold: * is a countably-additive measure on . * The measures are in some sense compatible under restriction of sequences: if , then . * If is in the projection of , the ultrapower by is wellfounded. An equivalent definition is produced when the final condition is replaced with the following: is said to be -homogeneous if each is -complete. Homogeneous trees are involved in Martin and Steel's proof of projective determinacy.
dcterms:subject
dbc:Descriptive_set_theory dbc:Determinacy
dbo:wikiPageID
9104798
dbo:wikiPageRevisionID
950661438
dbo:wikiPageWikiLink
dbr:Ultraproduct dbr:Tree_(descriptive_set_theory) dbr:Ultrafilter dbr:Descriptive_set_theory dbr:John_R._Steel dbr:Donald_A._Martin dbc:Determinacy dbr:Measure_(mathematics) dbr:Projective_determinacy dbc:Descriptive_set_theory
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dbo:abstract
In descriptive set theory, a tree over a product set is said to be homogeneous if there is a system of measures such that the following conditions hold: * is a countably-additive measure on . * The measures are in some sense compatible under restriction of sequences: if , then . * If is in the projection of , the ultrapower by is wellfounded. An equivalent definition is produced when the final condition is replaced with the following: * There are such that if is in the projection of and , then there is such that . This condition can be thought of as a sort of countable completeness condition on the system of measures. is said to be -homogeneous if each is -complete. Homogeneous trees are involved in Martin and Steel's proof of projective determinacy.
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wikipedia-en:Homogeneous_tree?oldid=950661438&ns=0
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2005
foaf:isPrimaryTopicOf
wikipedia-en:Homogeneous_tree
Subject Item
dbr:Homogeneously_Suslin_set
dbo:wikiPageWikiLink
dbr:Homogeneous_tree
Subject Item
wikipedia-en:Homogeneous_tree
foaf:primaryTopic
dbr:Homogeneous_tree