Definition:Class of All Ordinals

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The class of all ordinals is defined, obviously enough, as the class of all ordinals:

$\On = \leftset {x: x}$ is an ordinal $\rightset {}$

Therefore, by this definition, $A \in \On$ if and only if $A$ is an ordinal.

Also known as

The class of all ordinals is often referred to as the ordinal class, but this can be misconstrued as an ordinal class, which misrepresents it.

Also see

  • Results about the class of all ordinals can be found here.