# Searching for an analogue of ATR in the Weihrauch lattice

## TL;DR

This paper investigates whether an analogue of ATR_0 exists in the Weihrauch lattice, exploring various candidates and highlighting the complexity of establishing such a correspondence.

## Contribution

It systematically evaluates potential counterparts of ATR_0 in the Weihrauch degrees, revealing the challenges and intricacies involved.

## Key findings

- Multiple candidates for ATR_0 analogue are considered.
- No definitive counterpart for ATR_0 is identified.
- The relationship between reverse mathematics and Weihrauch degrees is complex.

## 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 ATR_0 has no identified counterpart in the Weihrauch degrees. We explore and evaluate several candidates, and conclude that the situation is complicated.