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Minor edit: corrected typo ("does" instead of "do") and added a small clarification to the explanation of why we want to avoid the intersections of all the lines of $Y_\alpha$ with $L_\alpha$

Minor edit: In the vector space example, the condition should be "the set of all $v_\beta$ that do not belong to the linear span of their predecessors", but it said "to the linear span of any of their predecessors", which may be interpreted as a lot of separated 1-dimensional spaces.

Completed premises of the lemma in the example for transfinite induction on countable ordinals. (Alpha needs to be a limit ordinal.)

Minor edit.

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