KnowraGödel's completeness theoremLinked fromLinked fromThe 21 pages that link to Gödel's completeness theorem, each with the reason it gives.All 21Broader topic 2Related 12Compared with 7Kurt GödelCompared with: It contrasts with incompleteness: first-order logic is complete even though arithmetic theories can be incomplete.SoundnessCompared with: Completeness reverses soundness's direction, from semantic validity to provability.Compactness theoremCompared with: For first-order logic, completeness supplies a proof route to compactness; the two properties are distinct.Second-order logicCompared with: No corresponding effective completeness theorem holds for full second-order validity.Gödel sentenceCompared with: It is a different Gödel result and concerns logic’s proof system, not arithmetic’s incompleteness.Herbrand's theoremCompared with: Both characterize first-order validity, but through different finite witnesses.Deduction theoremCompared with: It links semantic consequence to derivability rather than discharging a single assumption.