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

Julia Robinson has given a first-order definition of the rational integers$\mathbb Z$ in the rational numbers $\mathbb Q$ by a formula $(\forall \exists\forall \exists)(F=0)$ where the $\forall$-quantifiers run over a total of 8variables, and where F is a polynomial.  We show that for a large class of number fields, not including $\mathbb Q$,for every $\epsilon>0$, there exists a set of primes $\cal S$ of naturaldensity exceeding $1-\epsilon$, such that $\mathbb Z$ can be defined as asubset of the ``large'' subring $$\{x \in K : \ord_{\mathfrak p}x >0, \forall\mathfrak p \not \in \cal S \}$$ of K by a formula of the form $(\exists\forall \exists)(F=0)$ where there is only one $\forall$-quantifier, and whereF is a polynomial.

Defining the integers in large rings of number fields using one universal quantifier