Consistently $\mathcal P (\omega_1)$ is the union of less than $2^{\aleph_1}$ strongly independent families

by Komjath and Shelah. [KoSh:1080]

It is consistent that {P}(o_1) is the union of less than 2^{aleph_1} parts such that if A_0, ...,A_{n-1},B_0, ...,B_{m-1} are distinct elements of the same part then |A_0 cap ... cap A_{n-1} cap (o_1-B_0) cap ... cap (o_1-B_{m-1})|= aleph_1 .


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