A note on the diamond operator
Abstract
We show that if $1 \leq_W F$ and $F \star F \leq_W F$, then $F^\diamond \leq_W F$, where $\star$ and $\diamond$ are the following operations in the Weihrauch lattice: $\star$ is the compositional product, which allows the use of two principles in sequence, while the diamond operator $\diamond$ allows an arbitrary but finite number of uses of the given principle in sequence. This answers a question of Pauly.
 Publication:

arXiv eprints
 Pub Date:
 January 2020
 DOI:
 10.48550/arXiv.2001.09372
 arXiv:
 arXiv:2001.09372
 Bibcode:
 2020arXiv200109372W
 Keywords:

 Mathematics  Logic;
 03D30;
 03F60
 EPrint:
 5 pages