A student of Adi Jarden and mine attempts at generalizing results on selection principles from the Baire space $\omega^\omega$ to the higher Baire space $\kappa^\kappa$ ($\kappa$ uncountable), and similarly for the higher Cantor space $2^\kappa$, with the initial segment topology, as defined [here](https://mathoverflow.net/questions/233018/when-is-the-generalized-cantor-space-kappa-compact) and [here](https://mathoverflow.net/questions/234926/when-does-the-generalized-cantor-space-embed-in-a-kappa-compact-space). This leads (see linked questions) to many elementary questions whose answers are likely to be known.


We would appreciate references to surveys of this type of "higher descriptive set theory" and its basic results. In particular, it would be nice if these deal with results like Cantor-Bendixon Theorem, and combinatorial cardinals of the (higher) continuum.



References for higher descriptive set theory surveys
I would like suggest the following three course notes given by Sy Friedman:



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> 1) Invariant descriptive set theory (on classical and generalised Baire space),
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> 2) Cardinal characteristics of the uncountable,
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> 3) The higher descriptive set theory of isomorphism.
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Also the monograph



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> Generalised descriptive set theory and classification theory
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by Sy Friedman, Tapani Hyttinen and Vadim Kulikov must be very useful, in particular its introduction gives a survey of previously works on the subject.


All these papers are available at [Friedman's home page](http://www.logic.univie.ac.at/~sdf/papers/).


