Year: 2026
Type: preprint
Abstract: We give a relative consistency counterexample to the conjecture of Inamdar and Rinot that every regular uncountable cardinal carrying no amenable C-sequence is ineffable in the constructible universe L. The existence of a $Π^2_1$-indescribable cardinal is equiconsistent with the existence of a $Π^2_1$-indescribable cardinal carrying no amenable C-sequence and not ineffable in L. For every ground-model C-sequence on a weakly compact cardinal $κ$, generalized Hechler forcing adds a club D with $D\capβ\subseteq C_β$ at stationarily many inaccessible indices. We use this capture theorem in an iteration of length $κ^+$ after Johnstone's local lottery preparation.
Source: arXiv (Cornell University)
Author: Fernandes, Gabriel
Institution: Universidade de São Paulo
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221028314