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Cointerpretability

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Title: Cointerpretability  
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Subject: Mathematical Logic, Interpretability logic, Tolerant sequence, Mathematical relations, Index of logic articles
Collection: Mathematical Logic, Mathematical Relations
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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 Dzhaparidze (1993), who also proved that, for theories of Peano arithmetic and any stronger theories with effective axiomatizations, cointerpretability is equivalent to \Sigma_1-conservativity.

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