Generalized Continuum Hypothesis

Hypothesis
The Generalized Continuum Hypothesis is the proposition:

Let $x$ and $y$ be infinite sets.

Suppose:
 * $\phi_1: x \to y$ is injective

and:
 * $\phi_2: y \to \powerset x$ is injective

Then:
 * $y \sim x$ or $y \sim \powerset x$

In other words, there are no infinite cardinalities between $x$ and $\powerset x$.

Notation
The proposition may be abbreviated $\operatorname{GCH}$.