complete theory, negation completeness, omega-completeness, semantic completeness, syntactic completeness complete graph, complete inference system, complete lattice, complete metric space, complete partial ordering
a (logical) language is said to be complete iff all the formulas in the language that must be true (in any world in which the axioms of the language are true) can be proved from the axioms. Goedel's incompleteness theorem shows that any language in which the truths of basic arithmetic can be formulated cannot be complete (unless the number of axioms is {infinite).
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