Linked from

The 21 pages that link to Gödel's completeness theorem, each with the reason it gives.

• First-order logicRelated: It shows that semantic consequence in first-order logic has a matching proof system.

• Model theoryRelated: It equates truth in every structure with formal provability.

• Classical logicRelated: Gödel's completeness theorem links first-order validity with classical provability.

• Logical consequenceRelated: Completeness connects semantic consequence back to formal derivability.

• Mathematical logicRelated: It establishes that first-order proof rules capture semantic consequence.

• Kurt 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.

• Peano arithmeticRelated: It distinguishes provability in Peano arithmetic from truth in its standard model.

• EntscheidungsproblemRelated: Completeness ensures validity can be enumerated by proofs, even though it cannot be decided in general.

• Formal logicBroader topic: It establishes a precise match between semantic validity and formal proof for first-order logic.

• Foundations of mathematicsRelated: It distinguishes the completeness of first-order logic from the incompleteness of particular theories.

• Second-order logicCompared with: No corresponding effective completeness theorem holds for full second-order validity.

• CompletenessBroader topic: It establishes completeness for classical first-order logic.

• Consistency proofRelated: It connects syntactic consistency of first-order theories with having a model.

• Independence (mathematical logic)Related: It connects syntactic nonprovability with models that demonstrate independence.

• Löwenheim–Skolem theoremRelated: Completeness links syntactic consistency to model existence, a key setting for size arguments.

• 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.

• Lindenbaum's lemmaRelated: Lindenbaum extensions support the construction of models needed to prove this theorem.