Editing Cointerpretability

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.

==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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