Category:Definitions/Minimally Inductive Classes
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This category contains definitions related to Minimally Inductive Classes.
Related results can be found in Category: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 $\O$.
Pages in category "Definitions/Minimally Inductive Classes"
The following 4 pages are in this category, out of 4 total.