FOM: Re: topos axioms

[Colin McLarty]

Simpson wrote:

>  McLarty's "final draft" (6 Feb 1998 09:21:21) presents axioms for a
>  nontrivial Boolean topos, and for a well-pointed topos with natural
>  number object and choice.  But it doesn't present axioms for a
>  topos!  Why not?  Too hard to motivate from the f.o.m. perspective?

        Harvey's axioms for ZFC do not include the axiom of choice!
Why not? Too hard to motive from a fom perspective?

        Or is it rather that the axiom of choice is a trivial consequence of
his axioms, just as the topos axioms are trivial consequences of mine?