Cointerpretability

In mathematical logic, cointerpretability is a binary relation on formal theories: a formal theory T is cointerpretable in another such theory S, when the language of S can be translated into the language of T in such a way that S proves every formula whose translation is a theorem of T. The "translation" here is required to preserve the logical structure of formulas.

This concept, in a sense dual to interpretability, was introduced by Japaridze in 1993, who also proved that, for theories Peano arithmetic and any stronger theories with effective axiomatizations, cointerpretability is equivalent to <math>\Sigma_1<math>-conservativity.

See also: tolerance, cotolerance, interpretability logic.

References

• 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.