Extended set theory seems to be a very complicated mess simply to put tuples with column names on some sort of solid foundation. Why a structural set theory is not enough is unclear, although structural set theory certainly did not exist when Childs came up with his theory (some time in the 1970s).
See
http://www.dbms2.com/2010/06/05/extended-set-theory/
June 9th, 2010 11:31 am for some useful links.
http://www.xamuel.com/algebraix/is also useful.
These might explain what is the actual point of extended set theory
http://xsp.xegesis.org/Spio.pdf
http://xsp.xegesis.org/SSDAA.pdf