Extendible formulas in two variables in intuitionistic logic
Nick Bezhanishvili, Dick de Jongh

Abstract:
We give alternative characterizations of exact, extendible and
projective formulas in intuitionistic propositional calculus IPC in
terms of n-universal models. From these characterizations we derive a
new syntactic description of all extendible formulas of IPC in two
variables. For the formulas in two variables we also give an
alternative proof of Ghilardi’s theorem that every extendible formula
is projective.

Keywords: intuitionistic logic; universal models; exact formulas;
projective formulas; extendible