Studia Logica 108 (3):619-648 (2020)

Paolo Maffezioli
University of Barcelona
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 first-order logic with identity, as well as interpolation for several mathematical theories, including the theory of equivalence relations, partial and linear orders, and various intuitionistic order theories such as apartness and positive partial and linear orders.
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DOI 10.1007/s11225-019-09867-0
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Cut Elimination in the Presence of Axioms.Sara Negri & Jan Von Plato - 1998 - Bulletin of Symbolic Logic 4 (4):418-435.
Multicomponent Proof-Theoretic Method for Proving Interpolation Properties.Roman Kuznets - 2018 - Annals of Pure and Applied Logic 169 (12):1369-1418.

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