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.
Interpolation in singular geometric theories / Guido Gherardi; Paolo Maffezioli; Eugenio Orlandelli. - ELETTRONICO. - (2019), pp. 787-796. (Intervento presentato al convegno Proof-Thoeeoretic SemanticsAssessment and Future Perspectives tenutosi a University of Tuebingen nel 27-30 marzo 2019) [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.File | Dimensione | Formato | |
---|---|---|---|
GherardiMaffezioliOrlandelli_2019_InterpolSingGeomTh.pdf
accesso aperto
Tipo:
Versione (PDF) editoriale
Licenza:
Licenza per accesso libero gratuito
Dimensione
1.5 MB
Formato
Adobe PDF
|
1.5 MB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.