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Universal Formula


In predicate calculus, a universal 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 universally quantified.

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

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


See also

Existential Formula, Universal Quantifier

Portions of this entry contributed by Lorenzo Sauras-Altuzarra

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References

Carnap, R. Introduction to Symbolic Logic and Its Applications. New York: Dover, p. 34, 1958.Kirby, J. An Invitation to Model Theory. Cambridge, England: Cambridge University Press, 2019.

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Universal Formula

Cite this as:

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

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