| Version 6 |
Version 5 |
| A {\em limit cardinal} is a cardinal $\kappa$ such that $\lambda^+<\kappa$ for every cardinal $\lambda<\kappa$. Here $\lambda^+$ denotes the cardinal successor of $\lambda$. If $2^\lambda<\kappa$ for every cardinal $\lambda<\kappa$, then $\kappa$ is called a {\em strong limit cardinal}. Every strong limit cardinal is a limit cardinal, because $\lambda^+\leq2^\lambda$ holds for every cardinal $\lambda$. |
A {\em limit cardinal} is a cardinal $\kappa$ such that $\lambda^+<\kappa$ for every cardinal $\lambda<\kappa$. Here $\lambda^+$ denotes the cardinal successor of $\lambda$. If $2^\lambda<\kappa$ for every cardinal $\lambda<\kappa$, then $\kappa$ is called a {\em strong limit cardinal}. Every strong limit cardinal is a limit cardinal, because $\lambda^+\leq2^\lambda$ holds for every cardinal $\lambda$. |
| Under GCH every limit cardinal is a strong limit cardinal, because in this case $\lambda^+=2^\lambda$ for every infinite cardinal $\lambda$. |
Under GCH every limit cardinal is a strong limit cardinal, because in this case $\lambda^+=2^\lambda$ for every infinite cardinal $\lambda$. |
|
Note that some authors do not count $0$ as a (strong) limit cardinal. Some even exclude $\aleph_0$.
|
Note that some authors do not count $0$ as a limit cardinal. Some even exclude $\aleph_0$.
|
