Cofinalities of Marczewski-like ideals

TL;DR

This paper proves that the cofinalities of the Miller and Laver ideals are strictly larger than the continuum in ZFC, shedding light on their set-theoretic properties.

Contribution

It establishes that the cofinalities of these specific ideals exceed the continuum size within ZFC, a novel result in set theory.

Findings

Cofinalities of Miller and Laver ideals are larger than the continuum.

The result holds in ZFC without additional assumptions.

Advances understanding of the structure of these ideals.

Abstract

We show that the cofinalities of both the Miller ideal m^0 (the sigma-ideal naturally related to Miller forcing) and the Laver ideal ell^0 (related to Laver forcing) are larger than the size of the continuum in ZFC.