Page "Inaccessible cardinal" Paragraph 21

It is provable in ZF that ∞ satisfies a somewhat weaker reflection property, where the substructure ( V < sub > α </ sub >, ∈, U ∩ V < sub > α </ sub >) is only required to be ' elementary ' with respect to a finite set of formulas.

Ultimately, the reason for this weakening is that whereas the model-theoretic satisfaction relation can be defined, truth itself cannot, due to Tarski's theorem.