# Category:Minimally Inductive Classes

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.

## Pages in category "Minimally Inductive Classes"

The following 13 pages are in this category, out of 13 total.