Category:G-Tower is Well-Ordered under Subset Relation
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This category contains pages concerning 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.
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- G-Tower is Well-Ordered under Subset Relation
- G-Tower is Well-Ordered under Subset Relation/Corollary
- G-Tower is Well-Ordered under Subset Relation/Empty Set
- G-Tower is Well-Ordered under Subset Relation/Successor of Non-Greatest Element
- G-Tower is Well-Ordered under Subset Relation/Union of Limit Elements