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SUMMARY:On the binary linear ordering - Thilo Weinert (Udine)
DTSTART:20240522T150000Z
DTEND:20240522T160000Z
UID:TALK216028@talks.cam.ac.uk
CONTACT:Benedikt Loewe
DESCRIPTION:Let us call an order-type "untranscendable" if it cannot be em
 bedded into a product of two smaller ones (!). Ordinals are untranscendabl
 e if and only if they are multiplicatively\nindecomposable. Moreover untra
 nscendability almost implies additive indecomposability\, that is to say\,
  there is but one linear order type which is additively decomposable yet u
 ntranscendable. However\, using the Axiom of Choice one can prove that the
 re is a different untranscendable order type which at least fails to be st
 rongly indecomposable\, the order type of the real number continuum. Moreo
 ver\, we can show that there is nothing more among the sigma-scattered lin
 ear order types and consistently neither among the Aronszajn lines.\n\nTow
 ards the end of the talk I am going to sketch some open problems\, both in
  the presence and the absence of the Axiom of Choice.\n\nThis is joint ong
 oing work with Garrett Ervin and Alberto Marcone and builds on previous wo
 rk by Barbosa\, Galvin\, Hausdorff\, Laver\, Ranero\, and others.
LOCATION:Centre for Mathematical Sciences\, MR14
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