Category:Minimally Inductive Classes
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This category contains results about Minimally Inductive Classes.
Let $A$ be a class.
Let $g: A \to A$ be a mapping.
Definition 1
$A$ is minimally inductive under $g$ if and only if:
\((1)\) | $:$ | $A$ is inductive under $g$ | |||||||
\((2)\) | $:$ | No proper subclass of $A$ is inductive under $g$. |
Definition 2
$A$ is minimally inductive under $g$ if and only if:
\((1)\) | $:$ | $A$ is inductive under $g$ | |||||||
\((2)\) | $:$ | Every subclass of $A$ which is inductive under $g$ contains all the elements of $A$. |
Definition 3
$A$ is minimally inductive under $g$ if and only if $A$ is minimally closed under $g$ with respect to $\O$.
Subcategories
This category has the following 7 subcategories, out of 7 total.
M
N
Pages in category "Minimally Inductive Classes"
The following 13 pages are in this category, out of 13 total.
M
- Minimally Inductive Class under Progressing Mapping induces Nest
- Minimally Inductive Class under Progressing Mapping is Well-Ordered under Subset Relation
- Minimally Inductive Class under Progressing Mapping with Fixed Element is Finite
- Minimally Inductive Class under Slowly Progressing Mapping is Nest