On CON(${\mathfrak d}_\lambda >$ cov$_\lambda$(meagre))

TL;DR

This paper proves the consistency of a set-theoretic statement relating the dominating number and covering number of meagre sets at a strongly inaccessible cardinal, answering a question posed by Matet.

Contribution

It establishes the consistency of the dominating number exceeding the covering number of meagre sets at a strongly inaccessible cardinal, a previously open problem.

Findings

Dominating number can be made larger than cov_lambda(meagre) at certain cardinals.

Answers an open question by Matet about the relationship between these cardinal invariants.

Provides a consistency proof within set theory.

Abstract

We prove the consistency of: for suitable strongly inaccessible cardinal lambda the dominating number, i.e., the cofinality of ^{lambda}lambda, is strictly bigger than cov_lambda(meagre), i.e. the minimal number of nowhere dense subsets of ^{lambda}2 needed to cover it. This answers a question of Matet.