Axiom:Aleph Hypothesis

Axiom
The aleph hypothesis is the proposition:


 * $\aleph_{\alpha} = \beth_{\alpha}$ for all ordinals $\alpha$

where $\aleph_\alpha$ is the Aleph ($\aleph$) mapping and $\beth_\alpha$ is the Beth ($\beth$) mapping.

Notation
The Aleph hypothesis may be abbreviated $\operatorname{AH}$.