Editing Cointerpretability (section)

In [[mathematical logic]], '''cointerpretability''' is a [[binary relation]] on [[theory (mathematical logic)|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 {{harvtxt|Japaridze|1993}}, who also proved that, for theories of [[Peano arithmetic]] and any stronger theories with effective [[axiomatization]]s, cointerpretability is equivalent to <math>\Sigma_1</math>-conservativity.