If is a theory of
then it is consistent iff there is some model
of
such that
. If a theory is not consistent then it is inconsistent.
A slightly different definition is sometimes used, that is consistent iff
(that is, as long as it does not prove a contradiction). As long as the proof calculus used is sound and complete, these two definitions are equivalent.
This is version 3 of consistent, born on 2002-08-28, modified 2002-09-04.
Object id is 3386, canonical name is Consistent2.
Accessed 11147 times total.
