Cardinal invariants, non-lowness classes, and Weihrauch reducibility

Issue title: Oberwolfach Workshop on Computability Theory 2018

Guest editors: Vasco Brattka, Rod Downey, Julia F. Knight and Steffen Lempp

Article type: Research Article

Authors: Greenberg, Noam^{a; *} | Kuyper, Rutger^b | Turetsky, Dan^c

Affiliations: [a] Department of Mathematics, Victoria University of Wellington, Wellington, New Zealand. [email protected]; http://homepages.mcs.vuw.ac.nz/~greenberg/ | [b] Department of Mathematics, Victoria University of Wellington, Wellington, New Zealand | [c] Department of Mathematics, Victoria University of Wellington, Wellington, New Zealand. [email protected]

Correspondence: [*] Corresponding author. [email protected].

Abstract: We provide a survey of results using Weihrauch problems to find analogs between set theory and computability theory. In our treatment, we emphasize the role of morphisms in explaining these coincidences. We end with a discussion of the use of forcing to prove the nonexistence of morphisms.

Keywords: Cardinal invariants, Weihrauch reducibility, Turing degrees

DOI: 10.3233/COM-180219

Journal: Computability, vol. 8, no. 3-4, pp. 305-346, 2019