Logic Seminar
Sean Cox
VCU
Gorenstein Homological Algebra and elementary submodels
Abstract: The class of projective modules is central to classical
homological algebra. Relative homological algebra attempts to use
some class $\mathcal{G}$ and "do" homological algebra, but with
$\mathcal{G}$ playing the same role that the class of projectives
played in the original setting. However, an essential requirement for
this to work is that $\mathcal{G}$ be a "precovering" class (also
called a "right-approximating" class) of modules. There has been
considerable work in the last 20 years on the question of whether the
class of "Gorenstein Projective" modules is always a precovering class
(over every ring). While the question remains open, it is now known
that the answer is affirmative if there are enough large cardinals in
the universe. This was first proved by Saroch, and then
(independently) by me, using entirely different methods. I will
discuss some of the key ideas of my proof, especially the use of
(set-theoretic) "elementary submodel" arguments and Stationary Logic.
Tuesday February 2, 2021 at 4:00 PM in Zoom