Is the function symbol in first-order logic is the same as a function? If not, what is the definition of a function symbol?
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3No, it's just a given 'character' of first order formulas which syntactically are just strings of characters. All we have besides the symbol, is the arity of it, i.e. how many arguments it takes (in the syntax). – Berci Jan 13 '19 at 10:23
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See the post In Mathematical Logic, What is a Language? for example. – Mauro ALLEGRANZA Jan 14 '19 at 07:17