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Existential Formula


In predicate calculus, an existential formula is a prenex normal form formula (i.e., a formula written as a string of quantifiers and bound variables followed by a quantifier-free part) in which the quantified variables are existentially quantified.

Every existential formula is logically equivalent to the negation of some universal formula (and vice-versa).

When there are no free variables (i.e., when all the variables are bound) in an existential formula, it is called an existential sentence.


See also

Existential Quantifier, Universal Formula, Universal Sentence

Portions of this entry contributed by Lorenzo Sauras-Altuzarra

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References

Kirby, J. An Invitation to Model Theory. Cambridge, England: Cambridge University Press, 2019.

Cite this as:

Sauras-Altuzarra, Lorenzo and Weisstein, Eric W. "Existential Formula." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ExistentialFormula.html

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