We present 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.

Guido Gherardi, Paolo Maffezioli, Eugenio Orlandelli (2019). Interpolation in singular geometric theories. tuebingen : University of Tuebingen [10.15496/publikation-35319].

Interpolation in singular geometric theories

Guido Gherardi;Eugenio Orlandelli
2019

Abstract

We present 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.
2019
Proof-Theoretic Semantics: Assessment and Future Perspectives. Proceedings of the Third Tübingen Conference on Proof-Theoretic Semantics, 27–30 March 2019
787
796
Guido Gherardi, Paolo Maffezioli, Eugenio Orlandelli (2019). Interpolation in singular geometric theories. tuebingen : University of Tuebingen [10.15496/publikation-35319].
Guido Gherardi; Paolo Maffezioli; Eugenio Orlandelli
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/704717
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