The logic of linear tolerance

Studia Logica 51 (2):249 - 277 (1992)
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A nonempty sequence T1,...,Tn of theories is tolerant, if there are consistent theories T 1 + ,..., T n + such that for each 1 i n, T i + is an extension of Ti in the same language and, if i n, T i + interprets T i+1 + . We consider a propositional language with the modality , the arity of which is not fixed, and axiomatically define in this language the decidable logics TOL and TOL. It is shown that TOL (resp. TOL) yields exactly the schemata of PA-provable (resp. true) arithmetical sentences, if (A1,..., An) is understood as (a formalization of) PA+A1, ..., PA+An is tolerant.



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Citations of this work

Undecidability in diagonalizable algebras.V. Yu Shavrukov - 1997 - Journal of Symbolic Logic 62 (1):79-116.
Essential hereditary undecidability.Albert Visser - forthcoming - Archive for Mathematical Logic:1-34.

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Relative Interpretations.Steven Orey - 1961 - Mathematical Logic Quarterly 7 (7‐10):146-153.
Relative Interpretations.Steven Orey - 1961 - Mathematical Logic Quarterly 7 (7-10):146-153.

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