About: Tolerant sequence

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In mathematical logic, a tolerant sequence is a sequence ,..., of formal theories such that there are consistent extensions ,..., of these theories with each interpretable in . Tolerance naturally generalizes from sequences of theories to trees of theories. Weak interpretability can be shown to be a special, binary case of tolerance. This concept, together with its dual concept of , was introduced by Japaridze in 1992, who also proved that, for Peano arithmetic and any stronger theories with effective axiomatizations, tolerance is equivalent to -consistency.

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  • In mathematical logic, a tolerant sequence is a sequence ,..., of formal theories such that there are consistent extensions ,..., of these theories with each interpretable in . Tolerance naturally generalizes from sequences of theories to trees of theories. Weak interpretability can be shown to be a special, binary case of tolerance. This concept, together with its dual concept of , was introduced by Japaridze in 1992, who also proved that, for Peano arithmetic and any stronger theories with effective axiomatizations, tolerance is equivalent to -consistency. (en)
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  • In mathematical logic, a tolerant sequence is a sequence ,..., of formal theories such that there are consistent extensions ,..., of these theories with each interpretable in . Tolerance naturally generalizes from sequences of theories to trees of theories. Weak interpretability can be shown to be a special, binary case of tolerance. This concept, together with its dual concept of , was introduced by Japaridze in 1992, who also proved that, for Peano arithmetic and any stronger theories with effective axiomatizations, tolerance is equivalent to -consistency. (en)
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  • Tolerant sequence (en)
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