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A Mathematical Characterization of Interpretation between Theories

Johan van Benthem and David Pearce
Studia Logica: An International Journal for Symbolic Logic
Vol. 43, No. 3 (1984), pp. 295-303
Published by: Springer
Stable URL: http://www.jstor.org/stable/20015168
Page Count: 9
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A Mathematical Characterization of Interpretation between Theories
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Abstract

Of the various notions of reduction in the logical literature, relative interpretability in the sense of Tarski et al. [6] appears to be the central one. In the present note, this syntactic notion is characterized semantically, through the existence of a suitable reduction functor on models. The latter mathematical condition itself suggests a natural generalization, whose syntactic equivalent turns out to be a notion of interpretability quite close to that of Ershov [1], Szczerba [5] and Gaifman [2].

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