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/

Zendy Plus

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

Zendy Tools

Zendy Open

We present a new proof of the generalized {\L}o\'s-Tarski theorem($\mathsf{GLT}(k)$) introduced in [1], over arbitrary structures. Instead ofusing $\lambda$-saturation as in [1], we construct just the "requiredsaturation" directly using ascending chains of structures. We also strengthenthe failure of $\mathsf{GLT}(k)$ in the finite shown in [2], by strengtheningthe failure of the {\L}o\'s-Tarski theorem in this context. In particular, weprove that not just universal sentences, but for each fixed $k$, even$\Sigma^0_2$ sentences containing $k$ existential quantifiers fail to capturehereditariness in the finite. We conclude with two problems as futuredirections, concerning the {\L}o\'s-Tarski theorem and $\mathsf{GLT}(k)$, bothin the context of all finite structures.  [1] 10.1016/j.apal.2015.11.001 ; [2] 10.1007/978-3-642-32621-9\_22

Revisiting the generalized {\L}o\'s-Tarski theorem