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| In [[mathematical logic]], a '''cotolerant sequence''' is a sequence
| | The author's name is Ming Frerichs. Managing people has been my profession for for years. Badge collecting precisely what I do every weeks time. For a while he's been in South Dakota. If you want to gather more check out my website: http://euroseonet.hol.es/ |
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| :<math>T_1, \ldots, T_n</math>
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| of [[formal theory|formal theories]] such that there are [[consistent extension]]s <math>S_1, \ldots, S_n</math> of these theories with each <math>S_{i+1}</math> is [[cointerpretability|cointerpretable]] in <math>S_i</math>. Cotolerance naturally generalizes from sequences of theories to trees of theories.
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| This concept, together with its dual concept of [[tolerance (in logic)|tolerance]], was introduced by [http://www.csc.villanova.edu/~japaridz/ Japaridze] in 1992, who also proved that, for [[Peano arithmetic]] and any stronger theories with effective axiomatizations, tolerance is equivalent to <math>\Sigma_1</math>-consistency.
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| == See also ==
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| *[[Interpretability]]
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| *[[Cointerpretability]]
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| *[[Interpretability logic]]
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| ==References==
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| * [http://www.csc.villanova.edu/~japaridz/ G.Japaridze], ''The logic of linear tolerance''. Studia Logica 51 (1992), pp. 249–277.
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| * [http://www.csc.villanova.edu/~japaridz/study.html G.Japaridze], ''A generalized notion of weak interpretability and the corresponding logic''. Annals of Pure and Applied Logic 61 (1993), pp. 113–160.
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| * [http://www.csc.villanova.edu/~japaridz/study.html G.Japaridze] and D. de Jongh, ''The logic of provability''. '''Handbook of Proof Theory'''. S.Buss, ed. Elsevier, 1998, pp. 476–546.
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| [[Category:Logic]]
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| {{logic-stub}}
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Latest revision as of 11:02, 6 January 2015
The author's name is Ming Frerichs. Managing people has been my profession for for years. Badge collecting precisely what I do every weeks time. For a while he's been in South Dakota. If you want to gather more check out my website: http://euroseonet.hol.es/