Mathematical logic | Mathematical relations

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 , who also proved that, for theories of Peano arithmetic and any stronger theories with effective axiomatizations, cointerpretability is equivalent to -conservativity. (Wikipedia).

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Interpretability logic | Binary relation | Interpretability | Mathematical logic | Theory (mathematical logic) | Theorem