A formula is intuitionistically valid iff it is forced true by every world of every Kripke model.
A terminal world of a Kripke model (for intuitionistic logic) has a forcing relation equivalent to a classical model/interpretation.
If a given world (in a Kripke model (for intuitionistic logic)) forces neither nor then there is some possible "future" world (accessible from the "present" one) in which is forced true. In particular, if eventually becomes forced somewhere along any possible time thread (towards the "future"), then the present world would force to be true, but if this does not happen there there exists some possible future world in which becomes true.
Origin of kripke-model
- Named after Saul Kripke.