Is there a model of ${\sf ZF}$ such that there is an infinite set $X$ and a injective map $f:{\cal P}(X)\to {\cal P}(X)$ so that for $a\neq b \in {\cal P}(X)$ we have $|f(a)\cap f(b)| \leq 1$?
Model ${\sf ZF}$ that "spreads" members of ${\cal P}(X)$
Dominic van der Zypen
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