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Concept of the adequacy of a formal system that is employed both in proof theory and in model theory (seelogic). In proof theory, a formal system is said to be syntactically complete if and only if every closed sentence in the system is such that either it or its negation is provable in the system. In model theory, a formal system is said to be semantically complete if and only if every theorem of the system is provable in the system.
This entry comes from Encyclopædia Britannica Concise. For the full entry on completeness, visit Britannica.com.