Proposition 1. For every ordinal $\alpha$ there is a cardinal greater than $\alpha$.
Definition 1. The cardinal successor of an ordinal $\alpha$, denoted by $\alpha^+$, is the least cardinal greater than $\alpha$.
References
- [1]
- Wikipedia contributors. Successor cardinal. Wikipedia, The Free Encyclopedia.
- [2]
- Thomas Jech. Set Theory. 3rd Millennium ed, rev. and expanded. Springer, 2002. p. 29.