Year: 2026
Type: preprint
Abstract: We prove, in $\mathsf{ZFC}$, that the $λ$-terraced cube relation fails whenever $λ$ is an uncountable cardinal. The corresponding terraced relation for quadruples fails for every $λ$. If $λ$ is $\aleph_0$ then the pretinent terraced relation has consistency strength of at least one Woodin cardinal. We prove positive polarized relations at a successor and a double successor from wondrous ideals. We show, however, that there are no such ideals over two consecutive cardinals simultaneously.
Source: arXiv (Cornell University)
Author: Garti, Shimon
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Israel Science Foundation
Award: G2432433410
OpenAlex ID: W7212237697