Strong partition cardinal

From formulasearchengine
Jump to navigation Jump to search

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.


  • {{#invoke:citation/CS1|citation

|CitationClass=citation }}

  • {{#invoke:citation/CS1|citation

|CitationClass=citation }}.