Cotolerant sequence

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In mathematical logic, a cotolerant sequence is a sequence T_1, \ldots, T_n of formal theories such that there are consistent extensions S_1, \ldots, S_n of these theories with each S_{i+1} is cointerpretable in S_i. Cotolerance naturally generalizes from sequences of theories to trees of theories.

This concept, together with its dual concept of tolerance, was introduced by Japaridze in 1992, who also proved that, for Peano arithmetic and any stronger theories with effective axiomatizations, tolerance is equivalent to \Sigma_1-consistency.

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References[edit]

  • G.Japaridze, The logic of linear tolerance. Studia Logica 51 (1992), pp. 249–277.
  • G.Japaridze, A generalized notion of weak interpretability and the corresponding logic. Annals of Pure and Applied Logic 61 (1993), pp. 113–160.
  • G.Japaridze and D. de Jongh, The logic of provability. Handbook of Proof Theory. S.Buss, ed. Elsevier, 1998, pp. 476–546.