Editing Interpretability (section)

==Informal definition==
Assume ''T'' and ''S'' are [[Theory (mathematical logic)|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 [[Well-formed formula|formulas]].

This concept, together with [[weak interpretability]], was introduced by [[Alfred Tarski]] in 1953. Three other related concepts are [[cointerpretability]], [[tolerance (in logic)|logical tolerance]], and [[cotolerance]], introduced by [[Giorgi Japaridze]] in 1992–93.