Skolémisation

Definition

The skolemisation of a formula of the calculation of the predicates is a transformation of this formula consisting in replacing all the occurrences of the existential quantifier in occurrences of functions.

The version skolemized of a formula is not equivalent for him (the language being wide), nevertheless:

Tout model of the skolemized formula is model initial formula.

Tout model of the initial formula can be wide in a superstructure (by enrichment of the language with the introduced symbols of function) model of the skolemized formula.

Example

The formula $\backslash \; forall\; X\; \backslash \; exists\; R\; (X,\; there)$ is skolémisée there in $\backslash \; forall\; X\; R\; (X,\; F\; (X))$

See also

• Calculation of the predicates
• Theorem of Herbrand
• Theory of the models
• Model

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