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Title: Cotolerance  
Author: World Heritage Encyclopedia
Language: English
Subject: Index of logic articles, Cointerpretability
Publisher: World Heritage Encyclopedia


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 Peano arithmetic and any stronger theories with effective axiomatizations, tolerance is equivalent to \Sigma_1-consistency.

See also


  • 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.

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