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The 19 pages that link to Formal system, each with the reason it gives.

• David HilbertRelated: Formal systems became central to Hilbert’s program for grounding mathematics.

• AxiomNarrower topic: An axiom is one of the ingredients that makes a formal system.

• Rule of inferenceNarrower topic: Rules of inference operate within a system whose expressions and derivations are specified.

• Automated theorem provingRelated: A prover needs these components to define which conclusions count as proofs.

• Hilbert's programNarrower topic: Hilbert sought to encode mathematics as explicit axioms and derivation rules.

• Formal proofNarrower topic: A formal proof is a derivation inside such a system.

• Proof theoryNarrower topic: Proof theory studies derivations inside systems defined by explicit languages and rules.

• ConsistencyNarrower topic: Consistency is defined relative to a system’s axioms and inference rules.

• Kurt GödelNarrower topic: Gödel’s results apply to formal systems capable of expressing enough arithmetic.

• FormalismNarrower topic: Formalism interprets mathematical theories through systems of symbols and rules.

• DerivationNarrower topic: A derivation takes place within a system whose rules define permitted steps.

• Consistency proofNarrower topic: Consistency is a property of a formal system’s derivations.

• Self-referenceNarrower topic: Self-reference in mathematics depends on what a formal system can express and prove.

• Foundations of GeometryNarrower topic: Geometry becomes a formal theory when its language and deductions are made explicit.

• Philosophy of mathematicsRelated: Formal systems make precise what counts as a mathematical statement and derivation.

• Hilbert's axiomsRelated: Hilbert's axioms function as the starting statements of a geometric formal system.

• Formal scienceBroader topic: Formal sciences investigate structures built from explicit symbols and rules.

• Axiom (mathematics and logic)Narrower topic: An axiom has its role only within the system that adopts it.

• Mathematical conceptsRelated: Formal systems make precise the assumptions and rules underlying mathematical reasoning.