Completeness 「The eorem Suppose P is a noncontradictory path through a complete systematic tableau T from S with root Fa There is then a structure A in which a is false and every sentence in s is true
Completeness . Theorem . . Suppose P is a noncontradictory path through a complete systematic tableau τ from S with root Fα. There is then a structure A in which α is false and every sentence in S is true. Yi Li (Fudan University) Discrete Mathematics June 4, 2013 6 / 17
Completeness( Cont emma Let the notation be as above o If FB occurs on P, then B is false in A o If TB occurs on P, then B is true in A
Completeness(Cont.) . Lemma . . Let the notation be as above 1. If Fβ occurs on P, then β is false in A. 2. If Tβ occurs on P, then β is true in A. Yi Li (Fudan University) Discrete Mathematics June 4, 2013 7 / 17