Cardinal characteristic of the continuum

In the mathematical discipline of set theory, a cardinal characteristic of the continuum is an infinite cardinal number that may consistently lie strictly between ${\displaystyle \aleph _{0}}$ (the cardinality of the set of natural numbers), and the cardinality of the continuum, that is, the cardinality of the set ${\displaystyle \mathbb {R} }$ of all real numbers. The latter cardinal is denoted ${\displaystyle 2^{\aleph _{0}}}$ or ${\displaystyle {\mathfrak {c}}}$. A variety of such cardinal characteristics arise naturally, and much work has been done in determining what relations between them are provable, and constructing models of set theory for various consistent configurations of them.

...
Wikipedia