MathDBUltraexacting-above-extendible rank-Berkeley model conjecture
Ultraexacting-above-extendible rank-Berkeley model conjecture
Assume that holds, let be ultraexacting, and let be extendible.
Ultraexacting-above-extendible rank-Berkeley model conjecture. There is a set model of ZF with a rank-Berkeley cardinal.
This is the explicit formulation of the conjecture introduced in the concluding remarks. It strengthens the preceding consistency result from the paper's large-cardinal assumptions to the existence of an ultraexacting cardinal above an extendible cardinal, and is presented without a resolution.
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Sources & referencesView supporting material
Primary source
Juan P. Aguilera, Joan Bagaria and Philipp Lücke, “Large cardinals, structural reflection, and the HOD Conjecture”, arXiv:2411.11568 (2025).
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