On CON(Dominating_lambda > cov_\lambda(meagre))

TL;DR

This paper proves that for certain large cardinals, the dominating number exceeds the covering number of meager sets, answering a question posed by Matet.

Contribution

It establishes the consistency of the dominating number being strictly larger than the covering number of meager sets for suitable large cardinals.

Findings

Dominating number exceeds cov(meagre_lambda) for certain large cardinals.

Answers an open question by Matet.

Provides a consistency proof for the inequality.

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(meagre_lambda), i.e. the minimal number of nowhere dense subsets of 2^lambda needed to cover it. This answers a question of Matet.