Category:Semirings of Sets

This category contains results about Semirings of Sets.
Definitions specific to this category can be found in Definitions/Semirings of Sets.

Let $\SS$ be a system of sets.

$\SS$ is a semiring of sets or semi-ring of sets if and only if $\SS$ satisfies the semiring of sets axioms:

$(1)$	$:$			$\ds \O \in \SS $
$(2)$	$:$	$\cap$-stable	$\ds \forall A, B \in \SS:$	$\ds A \cap B \in \SS $
$(3)$	$:$		$\ds \forall A, A_1 \in \SS : A_1 \subseteq A:$	$\exists n \in \N$ and pairwise disjoint sets $A_2, A_3, \ldots, A_n \in \SS : \ds A = \bigcup_{k \mathop = 1}^n A_k$

Subcategories

This category has only the following subcategory.

The following 9 pages are in this category, out of 9 total.

\((1)\)	$:$			\(\ds \O \in \SS \)
\((2)\)	$:$	$\cap$-stable	\(\ds \forall A, B \in \SS:\)	\(\ds A \cap B \in \SS \)
\((3)\)	$:$		\(\ds \forall A, A_1 \in \SS : A_1 \subseteq A:\)	$\exists n \in \N$ and pairwise disjoint sets $A_2, A_3, \ldots, A_n \in \SS : \ds A = \bigcup_{k \mathop = 1}^n A_k$