21 Nov
2007
21 Nov
'07
2:33 p.m.
From Goedel's Theorem for HAH (higher order intuit. arithmetic) it follows
I also suspect that Sub(1) of the free topos with nno is not complete. But countability does not suffice for refuting completeness (the ordinal \omega + 1 is an infinite countable cHa which nevertheless is complete). that Sub(1) of the free topos with nno is not atomic. But that also doesn't suffice for refuting completeness. On p.169 of Freyd, Friedman and Scedrov's paper "Lindenbaum algebras of intuitionistic theories and free categories" (APAL 35) they claim "Lindenbaum algebras are almost never complete" but don't give a proof. Thomas Streicher