English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We prove that for every uncountable cardinal $\kappa$ such that$\kappa^{<\kappa}=\kappa$, the quasi-order of embeddability on the$\kappa$-space of $\kappa$-sized graphs Borel reduces to the embeddability onthe $\kappa$-space of $\kappa$-sized torsion-free abelian groups. Then we usethe same techniques to prove that the former Borel reduces to the embeddabilityon the $\kappa$-space of $\kappa$-sized $R$-modules, for every$\mathbb{S}$-cotorsion-free ring $R$ of cardinality less than the continuum. Asa consequence we get that all the previous are complete$\boldsymbol{\Sigma}^1_1$ quasi-orders.

The complexity of the embeddability relation between torsion-free abelian groups of uncountable size