Math 2.0

Mathematical logic and foundations Proof theory Concept

Proof theory

Builds on Mathematical proofPredicate logic

Summary

Proof theory is the branch of mathematical logic that treats proofs as mathematical objects. It studies formal proofs in systems of predicate logic and of arithmetic by combinatorial means. It began with Hilbert's aim to prove the consistency of mathematics by finitary methods. Its main tools include normal forms of proofs, cut elimination and ordinal analysis.

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Proposition, concept, no evidence levelPropositionconceptConjunction, definition, no evidence levelConjunctiondefinitionDisjunction, definition, no evidence levelDisjunctiondefinitionImplication, definition, no evidence levelImplicationdefinitionNegation, definition, no evidence levelNegationdefinitionPredicate, definition, no evidence levelPredicatedefinitionBiconditional, definition, no evidence levelBiconditionaldefinitionModus ponens, concept, no evidence levelModus ponensconceptMathematical proof, concept, no evidence levelMathematical proofconceptPropositional logic, concept, no evidence levelPropositional logicconceptPredicate logic, concept, no evidence levelPredicate logicconceptProof theory, concept, no evidence levelProof theoryconcept
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Proposition concept
  2. Conjunction definition
  3. Disjunction definition
  4. Implication definition
  5. Negation definition
  6. Predicate definition
  7. Biconditional definition
  8. Modus ponens concept
  9. Mathematical proof concept
  10. Propositional logic concept
  11. Predicate logic concept
  12. Proof theory concept

Where this leads

6 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Proof_theory
About this page
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Kindconcept
WritingW0 stub
MSC03F03, 03F05
UsesMathematical proof, Predicate logic
Same as
Changed2 November 2026

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