Intuitionistic axiomatizations for bounded extension Kripke models

Mohammad Ardeshir, Wim Ruitenburg, Saeed Salehi
2003 Annals of Pure and Applied Logic  
We present axiom systems, and provide soundness and strong completeness theorems, for classes of Kripke models with restricted extension rules among the node structures of the model. As examples we present an axiom system for the class of coÿnal extension Kripke models, and an axiom system for the class of end-extension Kripke models. We also show that Heyting arithmetic (HA) is strongly complete for its class of end-extension models. Coÿnal extension models of HA are models of Peano arithmetic (PA).
doi:10.1016/s0168-0072(03)00058-7 fatcat:qz3qtsbxczha7nqyobcvetxzou