User:Dfeuer/Definition:First-Order Formula
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Definition
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A logical formula $\varphi(A_1, A_2, \dots, A_n)$ is a first-order formula in the classes $A_1, A_2, \dots, A_n$ iff it quantifies only over sets.
That is, all bound variables in $\varphi$ are sets.
Sources
SF $\S 10$