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Arguments about derivability conditions are unnecessarily too specific #10

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iehality opened this issue Nov 28, 2024 · 0 comments
Open

Arguments about derivability conditions are unnecessarily too specific #10

iehality opened this issue Nov 28, 2024 · 0 comments

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@iehality
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iehality commented Nov 28, 2024 •
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（「代入を備えた論理」を整備してから取り掛かる予定）

現状 Incompleteness/DC はFirstOrder 上で定義されているが，sentence の証明に関する記法T ⊢!. σが煩雑，またその理論の強弱関係のinstance 関係が面倒になるなどの問題があり，一般に代入を備えた論理について述べたほうが簡潔になると思う．

このとき，ProvabilityPredicateは以下のようになる．

structure ProvabilityPredicate [System (F 0) S] (𝓢 𝓣 : S) where
  prov : F 1
  spec {σ : Sentence L} : T ⊢! σ → T₀ ⊢! prov/[⌜σ⌝]
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