Abstract
We prove a generalization of Maehara’s lemma to show that the extensions of classical and intuitionistic first-order logic with a special type of geometric axioms, called singular geometric axioms, have Craig’s interpolation property. As a corollary, we obtain a direct proof of interpolation for (classical and intuitionistic) first-order logic with identity, as well as interpolation for several mathematical theories, including the theory of equivalence relations, (strict) partial and linear orders, and various intuitionistic order theories such as apartness and positive partial and linear orders.
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Acknowledgements
We are very grateful to Birgit Elbl for precious comments and helpful discussions on various points. We also thank an anonymous referee for valuable suggestions that have helped to generalize our main result as well as to improve its exposition. Funding of Paolo Maffezioli by Alexander von Humboldt-Stiftung (Grant No. 3.3-ITA/1190393 STP).
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Gherardi, G., Maffezioli, P. & Orlandelli, E. Interpolation in Extensions of First-Order Logic. Stud Logica 108, 619–648 (2020). https://doi.org/10.1007/s11225-019-09867-0
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DOI: https://doi.org/10.1007/s11225-019-09867-0