A mathematical characterization of interpretation between theories

Studia Logica 43 (3):295-303 (1984)
Of the various notions of reduction in the logical literature, relative interpretability in the sense of Tarskiet 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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DOI 10.1007/BF02429844
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Alfred Tarski (1968/2010). Undecidable Theories. Amsterdam, North-Holland Pub. Co..

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