Absoluteness (mathematical logic)

In mathematical logic, a formula is said to be absolute if it has the same truth value in each of some class of structures. Theorems about absoluteness typically show that each of a large syntactic class of formulas is absolute. 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.
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