[FOM] Set Theory semantics

Rupert McCallum rupertmccallum at yahoo.com
Tue Oct 8 22:04:20 EDT 2002

On Wed, 2 Oct 2002 15:53:05 -0700 (PDT), I wrote:

> If it's only the first-order sentences you want reflected down to
> V_kappa, then in Kelly-Morse set theory we can actually prove there
> a countable ordinal with this property. 

Sorry that's incorrect, all you can prove is an ordinal of countable
cofinality with this property. It's actual size will depend on the
properties of the universe: if there is actually is an inaccessible, it
will have to dominate an inaccessible, etc.

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