Field of sets

https://en.wikipedia.org/wiki/Field_of_sets

A field of sets is a mathematical structure consisting of a pair ⟨X, 𝓕⟩ where X is a set and 𝓕 is a family of subsets of X called an algebra over X that contains the empty set as an element (identity), and is closed under the operations of taking complements in X, finite unions, and finite intersections.

Equivalently, an algebra over X is a subset 𝓕 of the power set of X such that

• ∅ ∈ 𝓕 (𝓕 has the identity element)

• ∀A ∈ 𝓕. A' ∈ 𝓕 (𝓕 is closed under compliment)

• ∀AB ∈ 𝓕. A B ∈ 𝓕 (𝓕 is closed under intersection)

• ∀AB ∈ 𝓕. A ∪ B ∈ 𝓕 (𝓕 is closed under union)