Effective Localization number: building $k$-surviving degrees

TL;DR

This paper develops effective versions of localization numbers, establishing hierarchies and analyzing their computational properties, and explores their relationships with other effective cardinal characteristics.

Contribution

It introduces effective localization numbers, constructs hierarchies, and examines their highness and computability properties in relation to known cardinal characteristics.

Findings

Proper hierarchies are produced.

Highness notions are relatively weak and often computably traceable.

Connections with other effective cardinal characteristics are discussed.

Abstract

We introduce and study effective versions of the localization numbers introduced by Newelski and Roslanowski (cite in paper). 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.