In mathematics, particularly in set theory, a **field of sets** (also known as a **system of sets**) is a collection of sets that is closed under certain operations. Specifically, a field of sets must satisfy the following properties: 1. **Contains the Universal Set**: The collection contains the universal set (the set containing all elements under consideration).
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A Boolean algebra of subsets contains the empty set and is closed under finite unions and complements. It is consequently closed under finite intersections, differences, and symmetric differences.