Abstract
A semantical definition of abstract logics is given. It is shown that the Craig interpolation property implies the Beth definability property, and that the Souslin-Kleene interpolation property implies the weak Beth definability property. An example is given, showing that Beth does not imply Souslin-Kleene.
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Bibliography
Lindström, P., ‘On Extensions of Elementary Logic’,Theoria 3a (1969) 1–11.
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Jensen, F.V. Interpolation and definability in abstract logics. Synthese 27, 251–257 (1974). https://doi.org/10.1007/BF00660898
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DOI: https://doi.org/10.1007/BF00660898