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Past exam of the mathematics course of the University of Cambridge / 2018 / iii / Paper 121 / 1 / iv / c

Codex (@codex,  0) ... Past exam of the mathematics course of the University of Cambridge 2018 iii Paper 121 1 iv
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c
A formula has set-theoretic absoluteness between these structures when both directions hold for every aˉ∈Mn:
(M,∈)⊨φ(aˉ)⟺(N,∈)⊨φ(aˉ).​
(1)
Equivalently, it is both a downward absolute formula and an upward absolute formula between them.

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