Editing Weak interpretability

In [[mathematical logic]], '''weak interpretability''' is a notion of translation of logical theories,  introduced together with [[interpretability]] by [[Alfred Tarski]] in 1953.

Let ''T'' and ''S'' be [[Theory (mathematical logic)|formal theories]]. Slightly simplified, ''T'' is said to be '''weakly interpretable''' in ''S'' if, and only if, the language of ''T'' can be translated into the language of ''S'' in such a way that the translation of every [[theorem]] of ''T'' is consistent with ''S''. 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]].

A generalization of weak interpretability, [[tolerance (in logic)|tolerance]], was introduced by [[Giorgi Japaridze]] in 1992. 

==See also==
*[[Interpretability logic]]

==References==
*{{citation
 | last = Tarski | first = Alfred | authorlink = Alfred Tarski
 | location = Amsterdam
 | mr = 0058532
 | publisher = North-Holland Publishing Company
 | series = Studies in Logic and the Foundations of Mathematics
 | title = Undecidable theories
 | year = 1953}}. Written in collaboration with [[Andrzej Mostowski]] and [[Raphael M. Robinson]].
*{{citation
 | last = Dzhaparidze | first = Giorgie | authorlink = Giorgi Japaridze
 | doi = 10.1016/0168-0072(93)90201-N
 | issue = 1-2
 | journal = Annals of Pure and Applied Logic
 | mr = 1218658
 | pages = 113–160
 | title = A generalized notion of weak interpretability and the corresponding modal logic
 | volume = 61
 | year = 1993| doi-access = 
 }}.
*{{citation
 | last = Dzhaparidze | first = Giorgie | authorlink = Giorgi Japaridze
 | doi = 10.1007/BF00370116
 | issue = 2
 | journal = Studia Logica
 | mr = 1185914
 | pages = 249–277
 | title = The logic of linear tolerance
 | volume = 51
 | year = 1992}}
*{{citation
 | last1 = Japaridze | first1 = Giorgi | author1-link = Giorgi Japaridze
 | last2 = de Jongh | first2 = Dick | author2-link = Dick de Jongh
 | editor-last = Buss | editor-first = Samuel R. | editor-link = Samuel Buss
 | contribution = The logic of provability
 | doi = 10.1016/S0049-237X(98)80022-0
 | location = Amsterdam
 | mr = 1640331
 | pages = 475–546
 | publisher = North-Holland
 | series = Stud. Logic Found. Math.
 | title = Handbook of Proof Theory
 | volume = 137
 | year = 1998| doi-access = free
 }}

[[Category:Proof theory]]