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.
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.