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Descriptive Set Theory is the study of definable subsets of Polish spaces, where definable is taken to mean from the Borel or projective hierarchies. Other topics include infinite games and determinacy, definable equivalence relations and Borel reductions between them, Polish groups, and effective descriptive set theory.
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Follow up question: Shelah's "Can you take Solovay's inaccessible away?"
In this answer to the question " Shelah's "Can you take Solovay's inaccessible away?" " the following is stated:
Assume that $\aleph_1$ is not inaccessible in $L$, hence a successor in $L$. So there …