Definable maximal cofinitary groups
Vera Fischer, Sy David Friedman, Asger T\"ornquist

TL;DR
This paper constructs a model of set theory where the continuum and bounding number are both , and a maximal cofinitary group with a -definable set of generators exists, using advanced forcing techniques.
Contribution
It introduces a method to produce a model with a -definable maximal cofinitary group alongside specific cardinal characteristics.
Findings
-sized continuum and bounding number in the model
Existence of a -definable set of generators for a maximal cofinitary group
Application of countable support iteration of S-proper posets
Abstract
Using countable support iteration of -proper posets, for some appropriate stationary set , we obtain a generic extension of the constructible universe, in which and there is a maximal cofinitary group with a -definable set of generators.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Mathematical and Theoretical Analysis
