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5 votes
3 answers
769 views

Cohen algebra (generalization)

Let Bor($X$) = class of all borel subsets of $X$. Cohen algebra is defined as Bor(X) modulo the ideal of meager sets. The Cohen algebra has a combinatorial : it is the unique atomless complete ...
Rina Shora's user avatar
4 votes
1 answer
746 views

Can all uncountable (but small) families of sets with positive measure have an uncountable subfamily with an intersection of positive measure?

My general question was is it consistent that any uncountable family of less than $\mathrm{non}(\mathcal{N})$ sets, each with positive measure, has an uncountable subfamily $\mathcal{F}$ s.t. $\bigcap ...
mtg's user avatar
  • 135
3 votes
1 answer
300 views

Measurably-isomorphic subsets of polish spaces and the continuum hypothesis

In Theorem 2.7 in the following notes, we seem to assume the following statement. Let $(\Omega,\mathcal F)$ be a Polish space, and $A\in\mathcal F$ an uncountable set. Then there exists a bijection ...
Dominic Wynter's user avatar