On CON(𝔡_{𝜆}> cov_{𝜆}(meagre))

Shelah, Saharon

doi:10.1090/tran/7948

On CON($\mathfrak {d}_\lambda >$ cov$_\lambda$(meagre))
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Trans. Amer. Math. Soc. 373 (2020), 5351-5369 Request permission

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.

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