Squares, scales and lines
Logic
2025-09-23 v1
Abstract
We use hypotheses from PCF theory to construct a linear ordering which has cardinality the successor of a singular cardinal of countable cofinality, and is incompact in the following sense: the ordering is not sigma-scattered, but every smaller subordering is sigma-wellordered. Such orderings were first constructed by Todorcevic using Jensen's square principle.
Keywords
Cite
@article{arxiv.2509.16755,
title = {Squares, scales and lines},
author = {James Cummings},
journal= {arXiv preprint arXiv:2509.16755},
year = {2025}
}