Codings of separable compact subsets of the first Baire class
| dc.creator | Dodos, Pandelis | |
| dc.date | 2008-05-14 | |
| dc.date.accessioned | 2026-07-07T09:38:48Z | |
| dc.date.available | 2026-07-07T09:38:48Z | |
| dc.description | Let $X$ be a Polish space and $K$ a separable compact subset of the first Baire class on $X$. For every sequence $\bs$ dense in $\kk$, the descriptive set-theoretic properties of the set \[ \lbf=\{L\in[\nn]: (f_n)_{n\in L} \text{is pointwise convergent}\} \] are analyzed. It is shown that if $K$ is not first countable, then $\lbf$ is $\PB^1_1$-complete. This can also happen even if $K$ is a pre-metric compactum of degree at most two, in the sense of S. Todorcevic. However, if $K$ is of degree exactly two, then $\lbf$ is always Borel. A deep result of G. Debs implies that $\lbf$ contains a Borel cofinal set and this gives a tree-representation of $\kk$. We show that classical ordinal assignments of Baire-1 functions are actually $\PB^1_1$-ranks on $\kk$. We also provide an example of a $\SB^1_1$ Ramsey-null subset $A$ of $[\nn]$ for which there does not exist a Borel set $B\supseteq A$ such that the difference $B\setminus A$ is Ramsey-null. | |
| dc.description | 24 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/0805.2026 | |
| dc.identifier | http://arxiv.org/abs/0805.2026 | |
| dc.identifier | Annals of Pure and Applied Logic, 142 (2006), 425-441 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/160942 | |
| dc.subject | Logic | |
| dc.subject | General Topology | |
| dc.subject | 03E15, 05D10, 26A21, 54H05 | |
| dc.title | Codings of separable compact subsets of the first Baire class | |
| dc.type | text |