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1. Oxford American Dictionary

   incompleteness theorem

   • IPA[ˌinkəmˈplētnis]

   • n.
     the theorem that in any sufficiently powerful, logically consistent formulation of logic or mathematics there must be true formulas which are neither provable nor disprovable. The theorem entails the corollary that the consistency of a logical system cannot be proved within that system.

   • noun: incompleteness theorem, plural noun: incompleteness theorems