Re: free variables in FOL

Ken Quirici wrote:

>
> How can free variables pop up at all in any sentential formulae?

I'm not sure what a sentential formula is, but one way to understand a
formula with free variables in it is to imagine that all the free
variables are bound by a prefix of universal quantifiers. So

F(x, y)

with x and y both free means one of these:

(all x)(all y) F(x, y)

(all y)(all x) F(x, y)

Since they are provably materially equivalent it doesn't matter which,
but for the sake of definiteness you could require that the variables in
the prefix are in alphabetical order.
.