Searching for an analogue of atr0 in the Weihrauch lattice

, &
Journal of Symbolic Logic 85 (3):1006-1043 (2020)
  Copy   BIBTEX

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.

Categories

Keywords

Reprint years

DOI

10.1017/jsl.2020.12

Other Versions

No versions found

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 106,506

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

The open and clopen Ramsey theorems in the Weihrauch lattice.Alberto Marcone & Manlio Valenti - 2021 - Journal of Symbolic Logic 86 (1):316-351.
THE WEIHRAUCH LATTICE AT THE LEVEL OF $\boldsymbol {\Pi }^11{-}\mathsf{CA}0$ : THE CANTOR–BENDIXSON THEOREM.Vittorio Cipriani, Alberto Marcone & Manlio Valenti - forthcoming - Journal of Symbolic Logic:1-39.
The Discontinuity Problem.Vasco Brattka - 2023 - Journal of Symbolic Logic 88 (3):1191-1212.
Weihrauch degrees, omniscience principles and weak computability.Vasco Brattka & Guido Gherardi - 2011 - Journal of Symbolic Logic 76 (1):143 - 176.
On Weihrauch reducibility and intuitionistic reverse mathematics.Rutger Kuyper - 2017 - Journal of Symbolic Logic 82 (4):1438-1458.
Weihrauch Goes Brouwerian.Vasco Brattka & Guido Gherardi - 2020 - Journal of Symbolic Logic 85 (4):1614-1653.
The characterization of Weihrauch reducibility in systems containing.Patrick Uftring - 2021 - Journal of Symbolic Logic 86 (1):224-261.
The Tree Pigeonhole Principle in the Weihrauch Degrees.Damir D. Dzhafarov, Reed Solomon & Manlio Valenti - forthcoming - Journal of Symbolic Logic:1-23.
Refining the Taming of the Reverse Mathematics Zoo.Sam Sanders - 2018 - Notre Dame Journal of Formal Logic 59 (4):579-597.
Completion of choice.Vasco Brattka & Guido Gherardi - 2021 - Annals of Pure and Applied Logic 172 (3):102914.

Analytics

Added to PP
2020-07-11

Downloads
35 (#721,813)

6 months
11 (#332,048)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Algebraic properties of the first-order part of a problem.Giovanni Soldà & Manlio Valenti - 2023 - Annals of Pure and Applied Logic 174 (7):103270.
Searching problems above arithmetical transfinite recursion.Yudai Suzuki & Keita Yokoyama - 2024 - Annals of Pure and Applied Logic 175 (10):103488.

View all 6 citations / Add more citations

References found in this work

Closed choice and a uniform low basis theorem.Vasco Brattka, Matthew de Brecht & Arno Pauly - 2012 - Annals of Pure and Applied Logic 163 (8):986-1008.
Subsystems of Second Order Arithmetic.Stephen G. Simpson - 1999 - Studia Logica 77 (1):129-129.
Effective Borel measurability and reducibility of functions.Vasco Brattka - 2005 - Mathematical Logic Quarterly 51 (1):19-44.

View all 11 references / Add more references