Category:G-Tower is Well-Ordered under Subset Relation

Let $M$ be a class.

Let $g: M \to M$ be a progressing mapping on $M$.

Let $M$ be a $g$-tower.

Then $M$ is well-ordered under the subset relation such that:

$(1)$	$:$	Smallest Element:	$\O$ is the smallest element of $M$
$(2)$	$:$	Immediate Successor:	the immediate successor of $x$ (if there is one) is $\map g x$
$(3)$	$:$	Limit Element:	every limit element is the union of its set of predecessors.

Pages in category "G-Tower is Well-Ordered under Subset Relation"

The following 5 pages are in this category, out of 5 total.