Re: [HoTT] regular and strong-limit universes

[Thomas Streicher <streicher@mathematik.tu-darmstadt.de>]

In set theory there are the Zermelo universes, namely the V_\lambda
for limit ordinals \lambda > \omega. They have nice closure properties
in particular closure under exponentiation but what they are lacking
are closure under replacement, i.e. for all A in U and f : A -> U the
image of f is in U. Type theoretically this corresponds to the
possibility of defining families in U by recursion over some A \in U.

On the other hand in realizability models modest sets from a universe U
with excellent closure properties, in particular for every A \in U and
B : A -> U its sum \Sigma(A,B) \in U again.

So it's very model dependent whether there exist small universes with
excellent closure properties. But of course Prop or Omega is not part
of such a universe.

Thomas

-- 
You received this message because you are subscribed to the Google Groups "Homotopy Type Theory" group.
To unsubscribe from this group and stop receiving emails from it, send an email to HomotopyTypeTheory+unsubscribe@googlegroups.com.
For more options, visit https://groups.google.com/d/optout.