Constructions
One way to construct limit cardinals is via the union operation: is a weak limit cardinal, defined as the union of all the alephs before it; and in general for any limit ordinal λ is a weak limit cardinal.
The ב operation can be used to obtain strong limit cardinals. This operation is a map from ordinals to cardinals defined as
- (the smallest ordinal equinumerous with the powerset)
- If λ is a limit ordinal,
The cardinal
is a strong limit cardinal of cofinality ω. More generally, given any ordinal α, the cardinal
is a strong limit cardinal. Thus there are arbitrarily large strong limit cardinals.
Read more about this topic: Limit Cardinal