A universal property for the ordinal Omega?

15 Sep 2000

      Has anybody ever proved the following result?

In the category of posets the initial algebra with the following
operations:

1- a constant 0

2- an inflationary successor s :  x \le sx

3- sups of omega-Chains

is the least non-denumerable ordinal  Omega.

This seems to be a pretty natural question to ask, so it must have been
done before.

Francois Lamarche