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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The generic ultrafilter $\mathcal{G}_2$ forced by $\mathcal{P}(\omega\times\omega)/($Fin$\otimes$Fin) was recently proved to be neither maximum nor minimum in the Tukey order of ultrafilters (in a recent paper of Blass, Dobrinen, and Raghavan), but it was left open where exactly in the Tukey order it lies. We prove that $\mathcal{G}_2$ is in fact Tukey minimal over its projected Ramsey ultrafilter. Furthermore, we prove that for each $k\ge 2$, the collection of all nonprincipal ultrafilters Tukey reducible to the generic ultrafilter $\mathcal{G}_k$ forced by $\mathcal{P}(\omega^k)/$Fin$^{\otimes k}$ forms a chain of length $k$. Essential to the proof is the extraction of a dense subset $\mathcal{E}_k$ from (Fin$^{\otimes k})^+$ which we prove to be a topological Ramsey space. The spaces $\mathcal{E}_k$, $k\ge 2$, form a hiearchy of high dimensional Ellentuck spaces. New Ramsey-classification theorems for equivalence relations on fronts on $\mathcal{E}_k$ are proved, extending the Pudlak-Rodl Theorem for fronts on the Ellentuck space, which are applied to find the Tukey structure below $\mathcal{G}_k$.

HIGH DIMENSIONAL ELLENTUCK SPACES AND INITIAL CHAINS IN THE TUKEY STRUCTURE OF NON-P-POINTS