2018/06/28 by Joel David Hamkins, Hamkins, Joel David, W. Hugh Woodin +1
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #math.LO
paper · pdf · doi:10.48550/arxiv.1806.11180
14 pages. Questions and commentary can be posted at http://jdh.hamkins.org/open-class-determinacy-preserved-by-forcing
arxiv created 2018/06/28 · openalex publication_date 2018/06/28 · arxiv updated 2018/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The principle of open class determinacy is preserved by pre-tame class forcing, and after such forcing, every new class well-order is isomorphic to a ground-model class well-order. Similarly, the principle of elementary transfinite recursion ETRΓ for a fixed class well-order Γ is preserved by pre-tame class forcing. The full principle ETR itself is preserved by countably strategically closed pre-tame class forcing, and after such forcing, every new class well-order is isomorphic to a ground-model class well-order. Meanwhile, it remains open whether ETR is preserved by all forcing, including the forcing merely to add a Cohen real.