Formally, a cardinal κ is called almost Ramsey iff for every functionf: κ < ω → {0, 1} (with κ < ω denoting the set of all finite subsets of κ) and for every λ < κ, there is a set of order type λ that is homogeneous for f.
This page is a list of some types of cardinals; it is arranged roughly in order of the consistency strength of the axiom asserting the existence of cardinals with the given property.
weakly and strongly inaccessible cardinals, α-inaccessible cardinals, and hyper inaccessible cardinals
weakly and strongly Mahlo cardinals, α-Mahlo cardinals, and hyper Mahlo cardinals.
Cardinal numbers, or cardinals for short, are numbers used to denote the size of a mathematical set.
It can also be proved that the cardinal (aleph-0, where aleph is the first letter in the Hebrew alphabet, represented by the unicode character and#1488;) of the set of natural numbers is the smallest infinite cardinal, i.e., that any infinite set admits a subset of cardinality .
The latter cardinal number is also often denoted by c; it is the cardinality of the set of real numbers, or the continuum, whence the name.
Feeds |
Contact