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SUMMARY:Sean Cox (VCU)
DTSTART:20210910T190000Z
DTEND:20210910T200000Z
DTSTAMP:20260423T035459Z
UID:VCU_ALPS/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VCU_ALPS/13/
 ">Undecidability of Salce's Problem for abelian groups</a>\nby Sean Cox (V
 CU) as part of VCU ALPS (Analysis\, Logic\, and Physics Seminar)\n\n\nAbst
 ract\nA cotorsion pair is a pair of classes $(\\mathcal{A}\,\\mathcal{B})$
  of abelian groups that is maximally orthogonal with respect to the EXT fu
 nctor.  This concept was introduced in an influential paper of Salce in th
 e 1970s\, where he asked whether every cotorsion pair is complete (the cot
 orsion pair $(\\mathcal{A}\,\\mathcal{B})$ is complete if every abelian gr
 oup is of the form $A/B$ for some $B \\in \\mathcal{B}$ and $A \\in \\math
 cal{A}$\; for example\, the cotorsion pair (Free abelian groups\, all abel
 ian groups) is complete).  I will discuss my recent proof that Salce's Pro
 blem is undecidable\, i.e.\, cannot be answered in the usual axioms of mat
 hematics.\n
LOCATION:https://researchseminars.org/talk/VCU_ALPS/13/
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