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

We study the relationship between non-trivial values of generalized cardinalinvariants at an inaccessible cardinal $\kappa$ and compactness principles at$\kappa^{++}$. We show that if the existence of a supercompact cardinal$\kappa$ with a weakly compact cardinal $\lambda$ above $\kappa$ is consistent,then the following are consistent as well (where $\mathfrak{t}(\kappa)$ and$\mathfrak{u}(\kappa)$ are the tower number and the ultrafilter number,respectively):  (i) There is an inaccessible cardinal $\kappa$ such that $\kappa^+ <\mathfrak{t}(\kappa)= \mathfrak{u}(\kappa)< 2^\kappa$ and stationary reflectionand the disjoint stationary sequence property at $\kappa^{++}$ hold.  (ii) There is an inaccessible cardinal $\kappa$ such that $\kappa^+ =\mathfrak{t}(\kappa) < \mathfrak{u}(\kappa)< 2^\kappa$ and the principles in(i) hold plus the tree property at $\kappa^{++}$ and the negation of the weakKurepa Hypothesis at $\kappa^+$.  The cardinals $\mathfrak{u}(\kappa)$ and $2^\kappa$ can have any reasonablevalues in these models. We compute several other values of cardinal invariants,such $\mathfrak{a}(\kappa)$ and $\mathfrak{b}(\kappa)$, and the invariants ofthe meager ideal (they are all equal to $\mathfrak{u}(\kappa)$). In (ii), wecompute $\mathfrak{p}(\kappa) = \mathfrak{t}(\kappa) = \kappa^+$ by observingthat the $\kappa^+$-distributive quotient of the Mitchell forcing adds a towerof size $\kappa^+$.  As a corollary of the construction, we obtain that (i) and (ii) are also truefor $\kappa = \omega$ (starting with a weakly compact cardinal in the groundmodel).

Generalized cardinal invariants for an inaccessible $\kappa$ with compactness at $\kappa^{++}$