Beth number

The Beth- function, named after the second letter of the Hebrew alphabet and also as written, is an enumeration, more precisely in the theory of cardinal numbers, used in the set theory sense of infinite cardinal numbers.

Definition

The Beth function assigns each ordinal a recursively defined as follows cardinal number to:

• , With the smallest infinite cardinal number, see Aleph function.
• For successor ordinals. Here is the right side for the power of cardinal numbers.
• For limit ordinals.

Comments

The continuum hypothesis is tantamount, because by definition, is the cardinality of the power set of a countable set and therefore equally powerful to the continuum. The generalized continuum hypothesis is equivalent to, that is, for all ordinals.

A limit cardinal number is called a strong limit if, for all cardinal numbers. A cardinal number is accurate then a strong limit cardinal number if. Limit for an ordinal