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SEARCHING FOR AN ANALOGUE OF ATR0 IN THE WEIHRAUCH LATTICE

Published online by Cambridge University Press:  10 July 2020

TAKAYUKI KIHARA
Affiliation:
DEPARTMENT OF MATHEMATICAL INFORMATICS NAGOYA UNIVERSITYNAGOYA, JAPANE-mail: kihara@i.nagoya-u.ac.jp
ALBERTO MARCONE
Affiliation:
DIPARTIMENTO DI SCIENZE MATEMATICHE, INFORMATICHE E FISICHE, UNIVERSITÁ DI UDINEUDINE, ITALYE-mail: alberto.marcone@uniud.it
ARNO PAULY
Affiliation:
DEPARTMENT OF COMPUTER SCIENCE SWANSEA UNIVERSITYSWANSEA, UK DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF BIRMINGHAMBIRMINGHAM, UKE-mail: Arno.M.Pauly@gmail.com

Abstract

There are close similarities between the Weihrauch lattice and the zoo of axiom systems in reverse mathematics. Following these similarities has often allowed researchers to translate results from one setting to the other. However, amongst the big five axiom systems from reverse mathematics, so far $\mathrm {ATR}_0$ has no identified counterpart in the Weihrauch degrees. We explore and evaluate several candidates, and conclude that the situation is complicated.

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Articles
Copyright
© The Association for Symbolic Logic 2020

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