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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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Of the various notions of reduction in the logical literature, relative interpretability in the sense of Tarski et al.  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 , Szczerba  and Gaifman .
Studia Logica: An International Journal for Symbolic Logic © 1984 Springer