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Full Idea
Kripke's variable domain approach to quantified modal logic famously invalidates the Barcan Formula.
Gist of Idea
The variable domain approach to quantified modal logic invalidates the Barcan Formula
Source
report of Saul A. Kripke (A Completeness Theorem in Modal Logic [1959]) by Ori Simchen - The Barcan Formula and Metaphysics §3
Book Ref
-: 'Theoria' [-], p.9
A Reaction
[p.9 and p.16] In a single combined domain all the possibilia must be present, but with variable domains objects in remote domains may not exist in your local domain. BF is committed to those possible objects.