In any Σ₁-complete theory containing PA, if the theory proves 'provability of φ implies φ', then it already proves φ. Generalises the second incompleteness theorem (take φ = ⊥). The modal schema □(□p → p) → □p characterises provability…
In any Σ₁-complete theory containing PA, if the theory proves 'provability of φ implies φ', then it already proves φ. Generalises the second incompleteness theorem (take φ = ⊥). The modal schema □(□p → p) → □p characterises provability…