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Let $\kappa$ be an infinite cardinal and let $B$ be the random forcing for adding $\kappa-$many random reals.

what are the elements of $B$.More precisely given a condition $p \in B$, what are the domain and the range of $p$, if there are any?. What does it mean "a coordinate of $p$"?.

edited Oct 28 2011 at 15:23

Todd Eisworth
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asked Oct 28 2011 at 15:13

Mohammad
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This question is more or less the same as this one: mathoverflow.net/questions/55832/… – Eran Oct 28 2011 at 17:12

I think that now there is somewhat of a stronger set theorists base in math.stackexchange.com that this question can be asked there instead. – Asaf Karagila Oct 28 2011 at 18:34

Goldstern · Answer 1 · 2011-10-28 15:49:20Z UTC

There are different ways of representing $B$. One possibility is to let $B$ consist of all closed subsets of $2^\kappa$ of positive measure; another possibility is to allow all positive Borel sets. Two conditions are equivalent if their symmetric difference has measure zero.

Each basic clopen set has a finite set of coordinates. By ccc, each open set is almost the same as some open set that uses only countably many coordinates. So every closed/Borel set $p$ is equivalent to a set that uses only countably many coordinates. I guess that these are the "coordinates of $p$".

random real forcing

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