Forcing and classes of $\mathsf{HYP}$-dominating functions

TL;DR

This paper investigates the computational power needed for certain forcing constructions, revealing a separation among three relativized non-lowness classes analogous to cardinals in Cichon's diagram.

Contribution

It introduces a new separation result among non-lowness classes related to Laver and Hechler forcing, connecting computability theory with set-theoretic cardinal characteristics.

Findings

Separated three relativized non-lowness classes.

Linked computational power to set-theoretic cardinals.

Provided insights into the complexity of forcing constructions.

Abstract

We study the question, what computational power is sufficient to perform constructions using either Laver or Hechler forcing. As a result, we obtain a separation between three relativised non-lowness classes that are the computability-theoretic analogues of three of the cardinals in Cichon's diagram.