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}

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- April 2nd 2013, 02:19 PMlain86Maximal consistent
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} - April 3rd 2013, 03:36 AMemakarovRe: Maximal consistent
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.