Undecidability of Salce's Problem for abelian groups

Sean Cox (VCU)

10-Sep-2021, 19:00-20:00 (3 years ago)

Abstract: A cotorsion pair is a pair of classes $(\mathcal{A},\mathcal{B})$ of abelian groups that is maximally orthogonal with respect to the EXT functor. This concept was introduced in an influential paper of Salce in the 1970s, where he asked whether every cotorsion pair is complete (the cotorsion pair $(\mathcal{A},\mathcal{B})$ is complete if every abelian group is of the form $A/B$ for some $B \in \mathcal{B}$ and $A \in \mathcal{A}$; for example, the cotorsion pair (Free abelian groups, all abelian groups) is complete). I will discuss my recent proof that Salce's Problem is undecidable, i.e., cannot be answered in the usual axioms of mathematics.

mathematical physicsanalysis of PDEsclassical analysis and ODEscategory theorycomplex variablesfunctional analysislogicmetric geometryoptimization and control

Audience: researchers in the topic


VCU ALPS (Analysis, Logic, and Physics Seminar)

Series comments: Description: Research seminar on topics ranging from analysis and logic to mathematical physics.

Meetings will be conducted over Zoom:

Meeting ID: 951 0562 0974

The password is 10 characters, consisting of the name of the ancient Greek mathematician who wrote "Elements" (first letter capitalized) followed by the first 4 primes.

Organizer: Ihsan Topaloglu*
Curators: Marco Aldi*, Brent Cody, Sean D. Cox, Alex Misiats, Allison Moore*
*contact for this listing

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