On CON(Dominating$_\lambda >$ cov(meagre))

We prove the consistency of: for suitable strongly
inaccessible cardinal lambda the dominating number,
i.e. the cofinaty of {}^lambda lambda is strictly bigger
than cov(meagre_lambda), i.e. the minimal number of
no-where-dense subsets of {}^lambda 2 needed to cover
it. This answers a question of Matet.

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