PreprintCC BY 4.0arXiv
Amenable C-sequences and ineffability in L
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 Π21-indescribable cardinal is equiconsistent with the existence of a Π21-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∩β⊆ Cβ at stationarily many inaccessible indices. We use this capture theorem in an iteration of length κ+ after Johnstone's local lottery preparation.
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BibTeX
@misc{fernandes2026amenable,
title = {{Amenable C-sequences and ineffability in L}},
author = {Gabriel Fernandes},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09086},
eprint = {2610.09086},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09086},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Amenable C-sequences and ineffability in L
AU - Gabriel Fernandes
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.09086
UR - https://arxiv.org/abs/2610.09086
AB - 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∩β⊆ C_β at stationarily many inaccessible indices. We use this capture theorem in an iteration of length κ^+ after Johnstone's local lottery preparation.
ER -