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.

C

Characteristics of Minimally Inductive Class under Progressing Mapping‎ (1 C, 4 P)

F

Fixed Point of Progressing Mapping on Minimally Inductive Class is Greatest Element‎ (3 P)

M

N

Non-Empty Bounded Subset of Minimally Inductive Class under Progressing Mapping has Greatest Element‎ (3 P)

S

Sandwich Principle for Slowly Progressing Mapping‎ (4 P)

Pages in category "Minimally Inductive Classes"

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

M

N

Non-Empty Bounded Subset of Minimally Inductive Class under Progressing Mapping has Greatest Element

S

V

Von Neumann Construction of Natural Numbers is Minimally Inductive