Re: Must higher-order logic be typed?

["Newberry"]

>
> However, if you ask "what is a higher order logic?" then one reasonable
> answer to that might be "a logic in which it is possible to quantify
> over sets or functions or predicates (not just over individuals)" and
> there are many logical systems in which this can be done but which are
> not typed (though they are not normally called higher order logics).
> The best known is set theory

This is what confuses me. Is set theory a multi-order logic done in a
first order logic?