 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 Σ_{1}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. 113160.
 G.Japaridze and D. de Jongh, The logic of provability. Handbook of Proof Theory. S.Buss, ed. Elsevier, 1998, pp. 476546.
This logicrelated article is a stub. You can help Wikipedia by expanding it.