In mathematics, a [binary] operation (like >, since it considers two natural numbers and then is either true or false, based on which numbers are considered) is just a set of ordered pairs.
Not to nitpick, but “>” is a binary relation, not a binary operation.
Not to nitpick, but “>” is a binary relation, not a binary operation.
Ha, thanks. I don’t mind nitpicking. I’ll edit the comment.
Actually, a binary relation is a binary operation (it returns 1 if true and 0 if false). You passed up a chance to counter-nitpick the nitpicker.
Yes, if you want a two-sorted theory, then you can make a boolean type and lift all relations to operations.
That’s not the typical use of the word “operation” in model theory, however.