Let Sigma={a,b,c}. Which of the following sets of formulae are maximal consistent?
(1){a,b,¬c}
(2){¬a∨b,b->c,¬c}
(3){¬b->a,¬a∨c}
(4){¬a∨b,b->c,¬c,a}
All except (4) are consistent. But shouldn't a maximally consistent set be infinite? For example, if A is in such a set, then so is A /\ A, A /\ A /\ A and so on.