Interpolation in extensions of first-order logic
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.
Cite
@article{arxiv.1807.11848,
title = {Interpolation in extensions of first-order logic},
author = {Guido Gherardi and Paolo Maffezioli and Eugenio Orlandelli},
journal= {arXiv preprint arXiv:1807.11848},
year = {2019}
}
Comments
In this up-dated version of the paper a more general notion of singular geometric theory is provided allowing the extension of our interpolation results to further fundamental mathematical theories