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# Absoluteness

<https://en.wikipedia.org/wiki/Absoluteness>

In mathematical logic, a formula is said to be **absolute** if it has the same truth value in each class of structures/models.

Theorems about absoluteness typically establish relationships between the absoluteness of formulas and their syntactic form.

There are two weaker forms of *partial absoluteness*:

* if the truth of a formula in each substructure `N` of a structure `M` follows from its truth in `M`, the formula is **downward absolute**.
* if the truth of a formula in a structure `N` implies its truth in each structure `M` extending `N`, the formula is **upward absolute**.