| Résume | In the spirit of the set-theoretic multiverse philosophy put forward by Joel David Hamkins, we explore a related modal multiverse populated by Kripke models and more general worlds. In this multiverse—as the talk will explain—the law of excluded middle can be switched on and off like a light bulb and countability is a button (for every set X of every world, there is a larger world containing a surjection ℕ → X). Our interest in this multiverse is because of concrete applications in commutative algebra and combinatorics, including the endeavor of extracting algorithms from proofs utilizing transfinite techniques. The talk will be framed by several examples of this kind. |
