Definition:G-Ordered Class

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Definition

Let $A$ be a class.

Let $g$ be a progressing mapping.

Let $A$ be well-ordered by the subset relation such that:

\((1)\)   $:$   the smallest element of $A$ is $\O$      
\((2)\)   $:$   every immediate successor $y$ is $\map g x$, where $x$ is the immediate predecessor of $y$      
\((3)\)   $:$   every limit element $x$ of $A$ is the union of the set of all predecessor elements of $x$      

Then $A$ is said to be $g$-ordered.


Also see

  • Results about $g$-ordered classes can be found here.


Sources