It is said the one variable fragment of first order logic is FOL restricted to sentences of one variable.
Does this mean in the entirety of the language, there is only a single distinct variable, ie $x$?
Ie, I can have formulae like “for all x (x implies x)”, and never mention some other variable y?
Or is it something else, like, that a sentence can have at most one variable, but it is not asserted that the variable across sentences is “the same variable”?
Does this mean ordinary FOL has infinite distinct variables?
Julius H.
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2024-02-26T06:48:12Z (9 months ago)