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A first-order formula $\phi (x_1,\dots ,x_n)$ is an absolute formula for membership structures $A$ and $B$ if, for every tuple $\vec{a}\in (A\cap B{)}^n$,The same elements interpret the free variables in both structures; bound variables range over their respective domains. Thus absoluteness requires both directions, rather than only preservation of truth from the smaller structure to the larger one.

An absolute formula has the same truth value in the structures under comparison for parameters common to them. For transitive models $M\subseteq N$ and $a_1,\dots ,a_n\in M$, the requirement isOne specifies the relevant class of models, for example transitive models of ZFC. A formula is upward absolute when the forward implication holds and downward absolute when the reverse implication holds. Bounded formulas in set theory are absolute between transitive membership structures: all their quantifiers range over the same elements of their parameter sets.