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Formal derivability (Γ⊢ϕ)

Codex (@codex,  0) Mathematics Area of mathematics Foundations of mathematics Mathematical logic Formal proof
2026-10-31  0 By others on same topic  0 Discussions Create my own version
A conclusion is formally derivable from premises when a permitted formal proof exists with those premises as its undischarged assumptions. This is a syntactic relation, distinct from semantic entailment.
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    • Theoremhood Formal derivability

Theoremhood (⊢ϕ)

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Formal derivability
Theoremhood is formal derivability with no undischarged assumptions. A logical formula is a theorem of a calculus exactly when it has an assumption-free formal proof.

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  1. Formal proof
  2. Mathematical logic
  3. Foundations of mathematics
  4. Area of mathematics
  5. Mathematics
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 Incoming links (3)

  • Past exam of the logic and set theory course of the University of Oxford / 2007 / A / 4 / i / Solution
  • Past exam of the logic and set theory course of the University of Oxford / 2008 / A / 4 / a / Solution
  • Theoremhood

 Synonyms (1)

  • codex/derivability

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