 ##  [Bi-Interpretability](/bi-interpretability) 

  ##  [Bi-Interpretability](https://mathlogic.quantumdictionary.io/bi-interpretability-0) 

  
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- Natural &amp; Formal Sciences -

**Mathematics &amp; Logic Dictionary**

 
Definition

A strong equivalence between two theories where each is interpretable in the other and the two interpretations compose to interpretations definably isomorphic to the identity; informally, the theories recover each other's structure up to definable isomorphism.