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The study of formal languages (sets of strings or trees over an alphabet), rewriting systems and algorithms, recognition automata/algorithms, and related questions.

2 votes

Does the fixed point lemma / diagonalization require capturing or not?

this trivially leads to inconsistency: We can show that if T ⊢ 𝝍 then T ⊢ ⊥, and likewise if T ⊢ ¬𝝍 then T ⊢ ⊥. In the case of $\neg\mathrm{Prov}(n)$, applying the diagonal lemma gives one (whe …
Benedict Eastaugh's user avatar