Completeness and Applications

Just as in the case of propositional logic we shall show that ‘derivability’ and ‘semantical consequence’ coincide. We will do quite a bit of work before we get to the theorem. Although the proof of the completeness theorem is not harder than, say, some proofs in analysis, we would advise the reader to read the statement of the theorem and to skip the proof at the first reading and to return to it later. It is more instructive to go to the applications and it will probably give the reader a better feeling for the subject.