Selection Principles in the Laver, Miller, and Sacks models

TL;DR

This paper explores how certain forcing models in set theory affect combinatorial properties of spaces, showing that in the Laver model, the Hurewicz property is preserved under finite products.

Contribution

It introduces a new result that in the Laver model, the Hurewicz property remains intact under finite products of metrizable spaces.

Findings

Hurewicz property is preserved in the Laver model

Interplay between forcing with fusion and covering properties

New instance of this interplay in set-theoretic topology

Abstract

This article is devoted to the interplay between forcing with fusion and combinatorial covering properties. We discuss known instances of this interplay as well as present a new one, namely that in the Laver model for the consistency of the Borel's conjecture, the Hurewicz property is preserved by finite products of metrizable spaces.