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

Reverse Mathematics is a program in the foundations of mathematics. Itprovides an elegant classification in which the majority of theorems ofordinary mathematics fall into only five categories, based on the 'Big Five'logical systems. Recently, a lot of effort has been directed towards findingexceptional theorems, i.e. which fall outside the Big Five. The so-calledReverse Mathematics zoo is a collection of such exceptional theorems (and theirrelations). It was shown in [17] that a number of uniform versions of thezoo-theorems, i.e. where a functional computes the objects stated to exist,fall in the third Big Five category arithmetical comprehension, insideKohlenbach's higher-order Reverse Mathematics. In this paper, we extend andrefine the results from [17]. In particular, we establish analogous results forrecent additions to the Reverse Mathematics zoo, thus establishing that thelatter disappear at the uniform level. Furthermore, we show that theaforementioned equivalences can be proved using only intuitionistic logic.Perhaps most surprisingly, these explicit equivalences are extracted fromnonstandard equivalences in Nelson's internal set theory, and we show that thenonstandard equivalence can be recovered from the explicit ones.

Refining the taming of the Reverse Mathematics zoo