In set theory, Θ (pronounced like the letter theta) is the least nonzero ordinal α such that there is no surjection from the reals onto α. If the axiom of choice (AC) holds (or even if the reals can be wellordered), then Θ is simply , the cardinal successor of the cardinality of the continuum. However, Θ is often studied in contexts where the axiom of choice fails, such as models of the axiom of determinacy. Θ is also the supremum of the lengths of all prewellorderings of the reals.
Property | Value |
---|---|
dbo:abstract |
|
dbo:wikiPageID |
|
dbo:wikiPageLength |
|
dbo:wikiPageRevisionID |
|
dbo:wikiPageWikiLink |
|
dbp:wikiPageUsesTemplate | |
dcterms:subject | |
rdf:type | |
rdfs:comment |
|
rdfs:label |
|
owl:sameAs | |
prov:wasDerivedFrom | |
foaf:isPrimaryTopicOf | |
is dbo:wikiPageRedirects of | |
is dbo:wikiPageWikiLink of |
|
is foaf:primaryTopic of |