Sentence (mathematical logic)

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In mathematical logic, a sentence is a formula with no free variables; it follows that, considering model theory, a sentence is either true or false in a given structure.

For example

is a sentence, and is false in the real numbers. (In plain English, its interpretation in the real numbers says that every real number has a real square root.) On the other hand,

is not a sentence, because of the presence of the free variable y; it will be true in the structure of the real numbers if y = 2, but not if y = − 2.

[edit] References

Hinman, P. (2005). Fundamentals of Mathematical Logic. A K Peters. ISBN 1-568-81262-0.