Codings of separable compact subsets of the first Baire class

Annals of Pure and Applied Logic 142 (1):425-441 (2006)
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Let X be a Polish space and a separable compact subset of the first Baire class on X. For every sequence dense in , the descriptive set-theoretic properties of the set are analyzed. It is shown that if is not first countable, then is -complete. This can also happen even if is a pre-metric compactum of degree at most two, in the sense of S. Todorčević. However, if is of degree exactly two, then is always Borel. A deep result of G. Debs implies that contains a Borel cofinal set and this gives a tree-representation of . We show that classical ordinal assignments of Baire-1 functions are actually -ranks on . We also provide an example of a Ramsey-null subset A of for which there does not exist a Borel set BA such that the difference BA is Ramsey-null



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[Omnibus Review].Yiannis N. Moschovakis - 1968 - Journal of Symbolic Logic 33 (3):471-472.
Every analytic set is Ramsey.Jack Silver - 1970 - Journal of Symbolic Logic 35 (1):60-64.

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