# Cointerpretability

Appearance

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 (1993), who also proved that, for theories of Peano arithmetic and any stronger theories with effective axiomatizations, cointerpretability is equivalent to -conservativity.

## See also

[edit]## References

[edit]- Japaridze, Giorgi (1993), "A generalized notion of weak interpretability and the corresponding modal logic",
*Annals of Pure and Applied Logic*,**61**(1–2): 113–160, doi:10.1016/0168-0072(93)90201-N, MR 1218658. - Japaridze, Giorgi; de Jongh, Dick (1998), "The logic of provability", in Buss, Samuel R. (ed.),
*Handbook of Proof Theory*, Studies in Logic and the Foundations of Mathematics, vol. 137, Amsterdam: North-Holland, pp. 475–546, doi:10.1016/S0049-237X(98)80022-0, MR 1640331.