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 Plus annual

Presents the access of premium content as premium feature

Premium Content

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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The ultrapower $T^{\ast}$ of an arbitrary ordered set $T$ is introduced as aninfinitesimal extension of $T$. It is obtained as the set of equivalenceclasses of the sequences in $T$, where the corresponding relation is generatedby an ultrafilter on the set of natural numbers. It is established that$T^{\ast}$ always satisfies Cantor's property, while one can give the necessaryand sufficient conditions for $T$ so that $T^{\ast}$ would be complete or itwould fulfill the open completeness property, respectively. Namely, the densityof the original set determines the open completeness of the extension, whileindependently, the completeness of $T^{\ast}$ is determined by the cardinalityof $T$.

Interval chains and completeness in ultrapowers of ordered sets