[FOM] n-th order ZFC

[meskew at math.uci.edu]

> From: Roger Bishop Jones <rbj at rbjones.com>
> Date: July 13, 2011 4:18:21 AM GMT+08:00
> To: Foundations of Mathematics <fom at cs.nyu.edu>
> Subject: Re: [FOM] n-th order ZFC
>
> In my view the important thing is not the drawing of
> philosophical questions, but the ability to express
> mathematical problems exactly which would otherwise require
> complications.
> For example, when we consider CH in  second order set theory
> we have a definite problem on our hands.
> When an author considers CH in a first order context it is
> often without any clear disambiguation of the problem.
> I dip occasionally into the literature surrounding CH and it
> is the norm even in informal overviews that I am unable to
> discover what problem is being addressed.
> Sometimes it is quite clear that the problem has not been
> pinned down, since V=L is admitted as one possible
> resolution of the problem, when to be strict it is rather
> one possible way of disambiguating the question (with the
> advantage that the problem is then already solved).

I don't see what the complication is.  In first order language one can
just ask, "Is CH true?"  The fact that there are different models that
think different things about CH does not prevent you from simply asking
whether CH is true in V.