[FOM] Re: Borel categoricity

Dave Marker marker at math.uic.edu
Fri Jul 18 19:33:40 EDT 2003

I appologize to all, I my last message was hasty

On Wed, 16 Jul 2003, Dave Marker wrote:

> This is known to be true, at least if T is omega-stable (or even stable).
> Under these assumptions, if there is a two cardinal model, there are
> arbitrarily large two-cardinal models (this is a theorem of Lachlan) and
> you can then use Erdos-Rado to build two cardinal models generated by
> indiscernibles. Using a set of indiscernibles of order type the reals
> yields a Borel two cardinal model.

What I meant was if a stable theory in a countable language has a two
cardinal model, then it has (\kappa,\aleph_0) models for arbitrarily
large \kappa. Now using Erdos-Rado...

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