From forcing to satisfaction in Kripke models of intuitionistic predicate logic. (English) Zbl 1492.03003
Summary: In this paper, we answer a natural question concerning the relation between forcing and satisfaction in Kripke models of intuitionistic predicate logic. We define a class of formulas denoted by \(\mathsf{R}^*\), with the property that forcing of any \(\mathsf{R}^*\)-formula in a node of a Kripke model of intuitionistic predicate logic implies its satisfaction in the classical structure attached to that node. We also prove that any formula with this property is an \(\mathsf{R}^*\)-formula.
MSC:
03B20 | Subsystems of classical logic (including intuitionistic logic) |
03C25 | Model-theoretic forcing |