Canonical first-order structure ($A=\{t^{\mathcal{A}}:t\text{ a closed term}\}$)

A canonical first-order structure is generated by closed-term names: each element is the interpretation of a closed term. In a first-order language without function symbols this says each element is named by a constant. The constant-name convention for canonical first-order structures agrees with this one in the function-free setting. Logical equality identifies different names for the same element.