Robin Hirsch, Ian Hodkinson, Maarten Marx, Szabolcs Mikulás, and
Mark Reynolds
Submitted to Memorial Volume for Elena Rasiowa, Studia Logica library,
Kluwer academic publishers, Dordrecht, 1997? 8 pages.
In an appendix to the Venema-Marx paper of the title [Report no. IR-396,
Faculteit der Wiskunde en Informatica, Vrije Universiteit Amsterdam, 1995],
we give a proof of completeness, decidability and finite base property
for the modal logic corresponding to the n-variable fragment of first-order
logic, with modal semantics relativised to 'locally cubic' sets of assignments
(worlds). All these results were already known, but the proofs we give
appear somewhat new and use a combinatorial theorem of Herwig.