The following set theoretical question is inspired by a question from recursion theory:

Question: Is there an $L$-random real $r$ which is a minimal cover over another real $x$?

Where a minimal cover $r$ over $x$ means that $x\in L[r] \wedge r\not\in L[x]$ but there is not real $z$ so that $x\in L[z]\wedge z\in L[r]\wedge r\not\in L[z]\wedge z\not\in L[x]$.

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