Short note on Sacks generic extensions
In this short note I give a simple and direct proof of the fact that a Sacks generic extension is generated by one Sacks real. A direct and detailed argument for this folkloric and well-known result is not to be found in most standard texts on this subject, including . In fact, I have only found one paper presenting a direct proof for this proposition (), but his argument is very short in the crucial part on the Cantor-Bendixon analysis. I provide here a more detailed argument, as I think that it is worth having this proof available to the nonspecialist.