Products of Hurewicz spaces in the Laver model

TL;DR

This paper explores the relationship between forcing with fusion and covering properties, showing that in the Laver model, the product of two Hurewicz spaces is Menger, linking set-theoretic forcing and topological properties.

Contribution

It proves that in the Laver model, the product of two Hurewicz spaces has the Menger property, establishing a new connection between forcing and topological covering properties.

Findings

In the Laver model, Hurewicz spaces' products are Menger.

The interplay between forcing with fusion and covering properties is demonstrated.

The result supports the consistency of certain topological properties under set-theoretic assumptions.

Abstract

This article is devoted to the interplay between forcing with fusion and combinatorial covering properties. We illustrate this interplay by proving that in the Laver model for the consistency of the Borel's conjecture, the product of any two metrizable spaces with the Hurewicz property has the Menger property.