In article <5fa54469-e270-4070-b2bc-90f35bb8ce49@p8g2000yqb.googlegroups.com>, "Ross A. Finlayson" <ross.finlayson@gmail.com> wrote:
> On Dec 1, 2:17 pm, Virgil <Vir...@home.esc> wrote: > > In article > > <f37ab501-a998-446b-8aaf-e88059d16...@z41g2000yqz.googlegroups.com>, > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 1 Dez., 20:46, Virgil <Vir...@home.esc> wrote: > > > > > > What makes you think that the elements of a limit set can be counted? > > > > > If the set exists, its elements exist and can be counted. > > > > That depends on what one means by "counting". Outside of > > Wolkenmuekenheim, there are sets which are not images of the naturals > > under any function, and such sets are uncountable. > > No, then you would have proven ZFC consistent.
Not outside of Wolkenmuekenheim, I wouldn't.
Ross seems to think that there are no uncountable sets in any set theory unless that set theory is embedded in ZFC.
