Random real forcing is the poset formed by the closed subsets of $[0,1]$ that are non-null (with respect to the Lebesgue measure), ordered by $\subseteq$.
Is the Random real forcing $\sigma$-linked?
Is the Random real forcing non-separative?
2026-03-27 18:37:03.1774636623
Is this presentation of the Random real forcing separative and $\sigma$-linked?
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Yes. Use the Lebesgue density theorem to find, for each condition $p$, an interval $(a,b)$ with rational endpoints such that the intersection $p\cap(a,b)$ has more than half of the measure of $(a,b)$.
Yes. Consider two conditions that differ by a set of measure $0$, for example $[0,\frac12]$ and $[0,\frac12]\cup\{\frac34\}$.