Title: On the smallest cardinality $\mathfrak q_0$ of a $Q$-set
Abstract: In this paper we collect some known information on the small uncountable cardinal $\mathfrak q_0$ defined as the smallest cardinality of a subset $A$ of the real line which fails to be a $Q$-set and hence contains a subset $B\subset A$ which is not of type $F_\sigma$ in $A$. We write down the proof of a folklore result that $\mathfrak p\le\mathfrak q_0\le\mathfrak b$ and refer to a result of Alan Dow on the consistency of the strict inequalities $\mathfrak p<\mathfrak q_0$ and $\mathfrak q_0<\mathfrak b$.
Publication Year: 2013
Publication Date: 2013-06-02
Language: en
Type: preprint
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