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Existential Sentence

An existential sentence is a statement claiming the existence of an object with given properties. In the language of set theory it can be formulated as follows,

exists x in U such that x in A,

where U is the universal set and A is a given set contained in it. In other words, it states that set A is nonempty.

See also

Existential Formula, Existential Quantifier, For Some, Sentence, Sufficiently Large, Universal Sentence

This entry contributed by Margherita Barile

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References

Carnap, R. Introduction to Symbolic Logic and Its Applications. New York: Dover, p. 34, 1958.Tarski, A. Introduction to Logic and to the Methodology of Deductive Sciences. New York: Oxford University Press, 1965.

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Existential Sentence

Cite this as:

Barile, Margherita. "Existential Sentence." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/ExistentialSentence.html

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