Squares, scales and lines

James Cummings (Carnegie Mellon U, Pittsburgh)

Jun 27. 2024, 14:00 — 14:45

Todorcevic showed that if kappa is singular of cofinality omega and square_kappa holds then there is a linear order of cardinality kappa^+ which is not sigma-scattered while all of its small suborders are sigma-wellordered. I will discuss how to get the same result from some pcf-theoretic principles, which follow both from weaker forms of square and from certain failures of SCH. If time allows I will discuss some related problems.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
Associated Event:
Determinacy, Inner Models and Forcing Axioms (Workshop)
Organizer(s):
Sandra Müller (TU Vienna)
Grigor Sargsyan (Polish Academy of Science, Warsaw)
Ralf Schindler (WWU Münster)
John Steel (UC, Berkeley)