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 define a function $\gamma:{\mathbb N} \to {\mathbb N}$ which eventuallydominates every computable function $\alpha:{\mathbb N} \to {\mathbb N}$. Weshow that there is a computer program which for $n \in {\mathbb N}$ prints thesequence $\{\gamma_i(n)\}_{i=0}^\infty$ of non-negative integers converging to$\gamma(n)$. We define a function $\beta:{\mathbb N} \to {\mathbb N}$ ofunknown computability which eventually dominates every function$\delta:{\mathbb N} \to {\mathbb N}$ with a single-fold Diophantinerepresentation. We show that there is a computer program which for $n \in{\mathbb N}$ prints the sequence $\{\beta_i(n)\}_{i=0}^\infty$ of non-negativeintegers converging to $\beta(n)$. Let ${\bf G}$ denote the followingstatement: $\exists f:{\mathbb N} \to {\mathbb N}$ of unknown computabilitysuch that $f$ eventually dominates every function $\delta:{\mathbb N} \to{\mathbb N}$ with a single-fold Diophantine representation and there is acomputer program which for $n \in {\mathbb N}$ prints the sequence$\{f_i(n)\}_{i=0}^\infty$ of non-negative integers converging to $f(n)$. Weshow that ${\bf G}$ has all properties from the title of the article.

A currently true statement G of the form "$\exists f:{\mathbb  N}\to{\mathbb N}$ of unknown computability ...", where $f$ is conjecturally  uncomputable, G remains unproven when $f$ is computable, and G holds forever  when $f$ is uncomputable