6 papers
Failure of the -dichotomy for generalized Cantor spaces
Matteo Casarosa, Philipp Schlicht
Kechris, Solecki and Todorčević's -dichotomy characterizes Borel graphs that admit a Borel measurable coloring with countably many colors. We show that the analogue to the $G_…
Nonvanishing derived limits from -type principles
Matteo Casarosa
Combinatorial set theory provides several tools to study derived limits of certain inverse systems of abelian groups. Most known nonvanishing results for with depend…
Higher limits of wider systems
Jeffrey Bergfalk, Matteo Casarosa
Write for what might be described as the most elementary nontrivial inverse system of abelian groups indexed by the functions from the cardinal to the set of nat…
Projective length, phantom extensions, and the structure of flat modules
Matteo Casarosa, Martino Lupini
We consider the natural generalization of the notion of the order of a phantom map from the topological setting to triangulated categories. When applied to the derived category of…
Simultaneously nonvanishing higher derived limits
Matteo Casarosa, Chris Lambie-Hanson
The derived functors of the inverse limit find many applications in algebra and topology. In particular, the vanishing of certain derived limits , pa…
Homological algebra of pro-Lie Polish abelian groups
Matteo Casarosa, Alessandro Codenotti, Martino Lupini
In this paper, we initiate the study of pro-Lie Polish abelian groups from the perspective of homological algebra. We extend to this context the type-decomposition of locally compa…