In set theory, the intersection of two sets is a set containing all elements that are members of both sets. The symbol, ∩, is used to indicate a set intersection.

For example, suppose that Γ and Δ are sets of formulae, as defined as:

- Γ = { α, β, φ }
- Δ = { β, φ, ρ, ω }

The intersection Γ ∩ Δ is therefore the following set:

- Γ ∩ Δ = { β, φ }

The intersection of two sets can be defined as follows:

- Γ ∩ Δ = {
*x*|*x*∈Γ ∧*x*∈Δ}

Which means, for any *x* that is an element of Γ ∩ Δ, *x* is an element of Γ, and *x* is a member of Δ.