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 {{harvtxt|Japaridze|1993}}, who also proved that, for theories of Peano arithmetic and any stronger theories with computable axiomatizations, cointerpretability is equivalent to <math>\Sigma_1</math>-conservativity.
==See also== * Cotolerance * Interpretability logic * Tolerance (in logic)
==References== *{{citation | last = Japaridze| first = Giorgi | authorlink = Giorgi Japaridze | doi = 10.1016/0168-0072(93)90201-N | issue = 1–2 | journal = Annals of Pure and Applied Logic | mr = 1218658 | pages = 113–160 | title = A generalized notion of weak interpretability and the corresponding modal logic | volume = 61 | year = 1993| doi-access = }}. *{{citation | last1 = Japaridze | first1 = Giorgi | author1-link = Giorgi Japaridze | last2 = de Jongh | first2 = Dick | author2-link = Dick de Jongh | editor-last = Buss | editor-first = Samuel R. | editor-link = Samuel Buss | contribution = The logic of provability | doi = 10.1016/S0049-237X(98)80022-0 | location = Amsterdam | mr = 1640331 | pages = 475–546 | publisher = North-Holland | series = Studies in Logic and the Foundations of Mathematics | title = Handbook of Proof Theory | volume = 137 | year = 1998| doi-access = free }}.
Category:Mathematical relations Category:Mathematical logic
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