Skip to main content
This website is in trial operation, support us!
We gratefully acknowledge support from all contributors.
Contribute Donate

Mathematics > Logic

arXiv:2406.02829v2 (math)
[Submitted on 5 Jun 2024 (v1) , last revised 26 Sep 2024 (this version, v2)]

Title: Approximation properties of torsion classes

Title: 挠类的逼近性质

Authors:Sean Cox, Alejandro Poveda, Jan Trlifaj
Abstract: We strengthen a result of Bagaria and Magidor~\cite{MR3152715} about the relationship between large cardinals and torsion classes of abelian groups, and prove that (1) the \emph{Maximum Deconstructibility} principle introduced in \cite{Cox_MaxDecon} requires large cardinals; it sits, implication-wise, between Vop\v{e}nka's Principle and the existence of an $\omega_1$-strongly compact cardinal. (2) While deconstructibility of a class of modules always implies the precovering property by \cite{MR2822215}, the concepts are (consistently) non-equivalent, even for classes of abelian groups closed under extensions, homomorphic images, and colimits.
Subjects: Logic (math.LO) ; Commutative Algebra (math.AC); Category Theory (math.CT); Rings and Algebras (math.RA)
Cite as: arXiv:2406.02829 [math.LO]
  (or arXiv:2406.02829v2 [math.LO] for this version)
  https://doi.org/10.48550/arXiv.2406.02829

Submission history

From: Sean Cox [view email]
[v1] Wed, 5 Jun 2024 00:27:50 UTC (11 KB)
[v2] Thu, 26 Sep 2024 15:50:56 UTC (12 KB)
Full-text links:

Access Paper:

view license
Current browse context:
math.LO
< prev   |   next >
new | recent | 2024-06
Change to browse by:
math
math.AC
math.CT
math.RA

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)
IArxiv Recommender (What is IArxiv?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)