Lindelöf spaces of singular density

István Juhász, Saharon Shelah

A cardinal $\lambda$ is called $\omega$-inaccessible if for all $\mu < \lambda$ we have $\mu^\omega < \lambda.$ We show that for every $\omega$-inaccessible cardinal $\lambda$ there is a CCC (hence cardinality and cofinality preserving) forcing that adds a hereditarily Lindelöf regular space of density $\lambda.$ This extends an analogous earlier result of ours that only worked for regular $\lambda$.

Key words and phrases: hereditarily Lindelöf space, density of a space, singular cardinal, forcing

2000 Mathematics Subject Classification: 54A25, 03E05

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