In article <LAW2-F281xrBXkkAWVr0001275d / hotmail.com>,
Ben Tilly <ben_tilly / hotmail.com> wrote:
>"Christoph Rippel" <crippel / primenet.com>  wrote:
>>(Besides their entertaining curiosity value for me;-)  RCO's
>>seem like very bad  ``type citizens'' - in many computer
>>languages you cannot form them and in math they are strictly
>>forbidden since they let to inconsistencies.
>
>Actually in many areas of math they are allowed.  But
>not in set theory.

  Not in *certain types* of set theory. Some recently
developed set theories allow them.  Cf. the book
_Vicious Circles_: On the Mathematics on Non-Wellfounded
Phenomena, by Jon Barwise and Lawrence Moss.

                        Regards, Bret
Bret Jolly
NB: my domain name does not have underbars or cow noises.