Axiomatic theories can prove all theorems from terms and axioms {completeness, mathematics}. For example, propositional calculus and predicate calculus are complete. Incomplete theories cannot prove at least one true statement from terms and axioms.
d-completeness
Complete theories can not allow new axioms {d-completeness}, because new axioms cause contradiction. For example, propositional calculus is d-complete. Predicate calculus is not d-complete, because it can add new axioms without contradicting any axiom or theorem and then use that axiom to prove more theorems.
Mathematical Sciences>Mathematics>Axiomatic Theory>Completeness
3-Mathematics-Axiomatic Theory-Completeness
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Date Modified: 2022.0224