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arXiv · 2509.16755

Squares, scales and lines

James Cummings
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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.

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James Cummings. 2025-09-20. Squares, scales and lines. https://arxiv.org/abs/2509.16755

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