Abstract
The Craig Interpolation Theorem is intimately connected with the emergence of abstract logic and continues to be the driving force of the field. I will argue in this paper that the interpolation property is an important litmus test in abstract model theory for identifying “natural,” robust extensions of first order logic. My argument is supported by the observation that logics which satisfy the interpolation property usually also satisfy a Lindström type maximality theorem. Admittedly, the range of such logics is small.
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Research partially supported by grant 40734 of the Academy of Finland.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Väänänen, J. The Craig Interpolation Theorem in abstract model theory. Synthese 164, 401–420 (2008). https://doi.org/10.1007/s11229-008-9357-z
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DOI: https://doi.org/10.1007/s11229-008-9357-z