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

A result of Kaufmann shows that if $L_\alpha$ is countable, admissible andsatisfies $\Pi_n\textsf{-Collection}$, then $\langle L_\alpha, \in \rangle$ hasa proper $\Sigma_{n+1}$-elementary end extension. This paper investigates towhat extent the theory that holds in $\langle L_\alpha, \in \rangle$ can betransferred to the partially-elementary end extensions guaranteed by Kaufmann'sresult. We show that there are $L_\alpha$ satisfying full separation, powersetand $\Pi_n\textsf{-Collection}$ that have no proper $\Sigma_{n+1}$-elementaryend extension satisfying either $\Pi_{n}\textsf{-Collection}$ or$\Pi_{n+3}\textsf{-Foundation}$. In contrast, we show that if $A$ is acountable admissible set that satisfies $\Pi_n\textsf{-Collection}$ and $T$ isa recursively enumerable theory that holds in $\langle A, \in \rangle$, then$\langle A, \in \rangle$ has a proper $\Sigma_n$-elementary end extension thatsatisfies $T$.

Partially-elementary end extensions of countable admissible sets