Using the compactness and completeness theorems

Godel’s completeness theorem (not to be confused with his incompleteness theorems) says that a theory has a model if and only if it is consistent, i.e. no contradiction is proved by the theory. This is the heart of model theory as it lets us answer questions about theories by looking at models and vice-versa.

One should not confuse the completeness theorem with the notion of a complete theory. A complete theory is a theory that contains every sentence or its negation.

— Wikipedia on Model theory

2012.09.20 Thursday ACHK