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completeness has no recorded synonym. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. Its one recorded opposite is incompleteness.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
the state of being complete and entire; having everything that is needed
(logic) an attribute of a logical system that is so constituted that a contradiction arises if any proposition is introduced that cannot be derived from the axioms of the system
Synonyms, antonyms and the broader and narrower relations for completeness come from Princeton University’s WordNet. Full sources and licences.