(3) Let L = {a, b, c, ?} where a, b, c are constant symbols and ? is a binary relation symbol. Let ? require that ? is a linear order and a ? c. Extend ? to ?* complete, consistent and saturated. Then define the term model M* and M*/? as in the Completeness Theorem.
(a) Suppose ?* requires a, b, c to be distinct and b ? a. Describe M* and M*/? (how many elements they contain and how their elements are ordered).
(b) Suppose ?* requires a = b ? c, b ? c, a ? b and b ? a. Describe M* and M*/? (you should notice that M* ? ?).