Effective localization number: Building k-surviving degrees

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: Ongay-Valverde, Iván^{a; *} | Schweber, Noah^b

Affiliations: [a] Department of Mathematics, University of Wisconsin–Madison, WI, USA. ongay@math.wisc.edu | [b] Department of Mathematics, University of Wisconsin–Madison, WI, USA. schweber@wisc.edu

Correspondence: [*] Corresponding author. ongay@math.wisc.edu.

Abstract: We introduce and study effective versions of the localization numbers introduced by Newelski and Roslanowski (Proceedings of the American Mathematical Society 117(3) (1993), 823–831). We show that proper hierarchies are produced, and that the corresponding highness notions are relatively weak, in that they can often be made computably traceable. We discuss connections with other better-understood effective cardinal characteristics.

Keywords: Set theory, computability theory, cardinal characteristics, Cichon diagram, forcing

DOI: 10.3233/COM-180199

Journal: Computability, vol. 8, no. 3-4, pp. 389-398, 2019