Given a normal modal logic, , a set, of formulae is said to be -consistent if , i.e., is not deducible from .
A set, , of formulae is said to be -maximal if it is consistent and, for any either or .
If is a -maximal set of formulae, then within the Lindenbaum-Tarski algebra, , the set is an ultrafilter.
Let , then is a bijection between and the set of ultrafilters of .
This set forms the set of states / worlds for the canonical frame of . The relations are given by
R_i \Gamma\Delta if, and only if, \Diamond_i\Delta \subseteq \Gamma.
Revised on November 5, 2010 07:59:06
by Tim Porter