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 1993), who also proved that, for theories of Peano arithmetic and any stronger theories with effective axiomatizations, cointerpretability is equivalent to [math]\displaystyle{ \Sigma_1 }[/math]-conservativity.

See also

• Cotolerance
• Interpretability logic.
• Tolerance (in logic)

References

• "A generalized notion of weak interpretability and the corresponding modal logic", Annals of Pure and Applied Logic 61 (1–2): 113–160, 1993, doi:10.1016/0168-0072(93)90201-N .
• "The logic of provability", Handbook of Proof Theory, Studies in Logic and the Foundations of Mathematics, 137, Amsterdam: North-Holland, 1998, pp. 475–546, doi:10.1016/S0049-237X(98)80022-0 .