List of large cardinal properties

This page includes a list of large cardinal properties in the mathematical field of set theory. It is arranged roughly in order of the consistency strength of the axiom asserting the existence of cardinals with the given property. Existence of a cardinal number κ of a given type implies the existence of cardinals of most of the types listed above that type, and for most listed cardinal descriptions φ of lesser consistency strength, Vκ satisfies "there is an unbounded class of cardinals satisfying φ".

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