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Title: Interpretability  
Author: World Heritage Encyclopedia
Language: English
Subject: Tolerant sequence, Weak interpretability, Interpretability logic, Cointerpretability, Ω-consistent theory
Publisher: World Heritage Encyclopedia


In mathematical logic, interpretability is a relation between formal theories that expresses the possibility of interpreting or translating one into the other.

Informal definition

Assume T and S are formal theories. Slightly simplified, T is said to be interpretable in S if and only if the language of T can be translated into the language of S in such a way that S proves the translation of every theorem of T. Of course, there are some natural conditions on admissible translations here, such as the necessity for a translation to preserve the logical structure of formulas.

This concept, together with Giorgi Japaridze in 1992-1993.


  • Japaridze, G., and De Jongh, D. (1998) "The logic of provability" in Buss, S., ed., Handbook of Proof Theory. North-Holland: 476-546.
  • Alfred Tarski, Andrzej Mostowski, and Raphael Robinson (1953) Undecidable Theories. North-Holland.

See also

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