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The 10 pages that link to Consistency proof, each with the reason it gives.

• Gödel's incompleteness theoremsRelated: The second theorem makes any consistency proof for arithmetic necessarily non-elementary.

• Non-Euclidean geometryRelated: Relative consistency arguments showed Euclidean and hyperbolic geometry could coexist as formal systems.

• Hilbert's programRelated: Gödel's second theorem showed why a system of sufficient strength cannot prove its own consistency.

• Proof theoryRelated: Constructing and calibrating consistency proofs is a longstanding proof-theoretic aim.

• ConsistencyBroader topic: It directly establishes the property defined by consistency.

• Peano arithmeticRelated: Gödel's second theorem limits what Peano arithmetic can prove about its own consistency, assuming it is consistent.

• FormalismRelated: Hilbert's program made consistency proofs a central goal for formalized mathematics.

• Foundations of GeometryRelated: Consistency proofs assess whether a geometric axiom system is logically safe under stated assumptions.

• Axiomatic systemRelated: Consistency proofs address whether the system's derivations avoid contradiction.

• Cut-elimination theoremRelated: Cut elimination can establish consistency by showing that contradiction has no cut-free derivation.