Ultrafilters in modal logic

From: Mike Carroll (mcarroll_at_pobox.com)
Date: 08/05/04 

Date: 5 Aug 2004 15:38:26 -0700

Recently Chris Menzel, in response to a question of mine, directed me
to an obscure paper by a well-known author:
Bas C. van Fraassen, "Compactness and Lowenheim-Skolem Proofs in Modal
Logic", Logique et Analyse 12(1969), pp. 167-178.

Having at last obtained a copy, I was surprised to find that the
proofs use ultrafilters. I'm familiar with ultrafilters from e.g.
Chang & Keisler's text "Model Theory", but have not seen them used in
any other discussions of modal logic. They're not mentioned in the
Hughes & Cresswell texts, for example.

Anybody know of other references to ultrafilters in model theory for
modal logic?

Mike Carroll
Oro Valley, AZ