# Category:Semirings of Sets

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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.

## Pages in category "Semirings of Sets"

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