Closed Sentential Formula
A closed sentential formula is a sentential formula in which none of the variables are free (i.e., all variables are bound). Examples of closed sentential formulas are given by
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which expresses the commutativity of addition, and
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which expresses the infinitude of the primes.
A closed sentential formula is called a sentence (Carnap 1958, pp. 24-25 and 85). However, in some language systems, open sentential formulas are also admitted as sentences (Carnap 1958, p. 25).
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