Set-theoretic Inevitability (with Cesare Straffelini)
Published in The Review of Symbolic Logic (accepted), 2026
Recommended citation: Scambler, Chris and Cesare Straffelini. (2026). "Set-theoretic Inevitability." The Review of Symbolic Logic (accepted for publication). arXiv:2610.31040. https://arxiv.org/abs/2610.31040
After defining the concept of inevitability for statements with the modal logic of forcing, we raise the question of which statements are inevitable under ZFC and under large cardinal hypotheses. We establish inevitability results concerning the perfect set property and Projective Determinacy, and discuss their conceptual significance for the foundations of set theory.