Definable maximal cofinitary groups

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 $S$-proper posets, for some appropriate stationary set $S$, we obtain a generic extension of the constructible universe, in which $\mathfrak{b}=\mathfrak{c}=\aleph_2$ and there is a maximal cofinitary group with a $\Pi^1_2$-definable set of generators.