due Thursday, Feb 20, 2003
Please read Smullyan, Chapter XI, p. 101-108 for Tuesday, February 18
Show that a set is consistent and complete if and only if it is maximally consistent.
Let be a consistent set
and {
,
, ...} be the set of all propositional variables.
Construct an infinite sequence of sets
as follows:
:= {}
:=
Define :=
. Show that there is exactly one interpretation v
that satisfies
and that
is uniformly satisfied by v
.