The Barcan Formula and Our Talk of Possible Worlds

You can find a short presentation on the Barcan formula and possible world semantics that I prepared, for the mathematics department day at IISER-K in 2024, here. I aimed to introduce modal notions and show that adding the tableaux rules for propositional modal logic and classical first order logic leads to a logic which validates the Barcan formula (constant domain system). I also mention a counter example from varying domain semantics and explain why free logic is used instead of classical first order logic.