Cotolerant sequence

Cotolerant sequence

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 $Σ 1$ -consistency.

See also

References

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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