Squares, scales and lines

2025/09/20 by Cummings, James
#03E35 (Primary) (Secondary) 06A05 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2509.16755

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.

Related

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• On minimal non-σ-scattered linear orders
• Keisler's Order is Not Linear, Assuming a Supercompact
• PCF theory: applications
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