Given a unital theory 𝕋 𝕋 \mathbb{T} and a family X i subscript 𝑋 𝑖 X_{i} of 𝕋 𝕋 \mathbb{T} models, the direct sum ⨁ X i direct-sum subscript 𝑋 𝑖 \bigoplus X_{i} consists of finitely supported functions ( i : I ) → X i (i:I)\to X_{i} .