User blog comment:KthulhuHimself/Norminals Revisited./@comment-1605058-20151207205051

I have just realized that I've made a mistake when I was explaining predicates to you over IRC yesterday, which I'm sorry about and which I want to correct now.

I have said that "Predicate is any formula in the language with exactly one free variable". What I should have said is that a predicate is a certain propositional function, i.e. a function from the domain of discourse (in case of FOST - the universe of sets) to the set {true, false}, or to say another way - it describes a property which every element of the domain of discourse can either satisfy or not satisfy. If we denote the predicate by P, then P(x) states whether x has this property or not.

This isn't the same thing as I told you because now we don't require P to be defined by any formula.