Year: 2026
Type: preprint
Abstract: Starting from a model of $\mathrm{ZFC}$, we force the simultaneous failure of the Very Weak Club Guessing and the $\mho$ principles at $S_κ^{κ^+}$, for any regular cardinal $κ$. Our results are obtained by means of a forcing iteration technique, due to Krueger, that incorporates models as side conditions. At $ω_1$, the failure of these principles is a well-known consequence of $\mathrm{PFA}$.
Source: arXiv (Cornell University)
Author: Gallart, Curial
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Austrian Science Fund
OpenAlex ID: W7203732497