Codings of separable compact subsets of the first Baire class

Dodos, P

dc.contributor.author	Dodos, P	en
dc.date.accessioned	2014-03-01T01:23:42Z
dc.date.available	2014-03-01T01:23:42Z
dc.date.issued	2006	en
dc.identifier.issn	0168-0072	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/17101
dc.subject	Baire class one functions	en
dc.subject	Pointwise convergent sequences	en
dc.subject	Separable compacta	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Mathematics	en
dc.subject.other	ANALYTIC SETS	en
dc.subject.other	BANACH-SPACES	en
dc.subject.other	CLASSIFICATION	en
dc.title	Codings of separable compact subsets of the first Baire class	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.apal.2006.05.006	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.apal.2006.05.006	en
heal.language	English	en
heal.publicationDate	2006	en
heal.abstract	Let X be a Polish space and kappa a separable compact subset of the first Baire class on X. For every sequence f = (f(n))(n) dense in kappa, the descriptive set-theoretic properties of the set L-f = {L epsilon [N] : (f(n))(n epsilon L) is pointwise convergent} are analyzed. It is shown that if kappa is not first countable, then L-f is Pi(1)(1)-complete. This can also happen even if kappa is a pre-metric compactum of degree at most two, in the sense of S. Todorcevic. However, if kappa is of degree exactly two, then Lf is always Borel. A deep result of G. Debs implies that L-f contains a Borel cofinal set and this gives a tree-representation of kappa. We show that classical ordinal assignments of Baire-1 functions are actually Pi(1)(1)-ranks on kappa. We also provide an example of a Sigma(1)(1) Ramsey-null subset A of [N] for which there does not exist a Borel set B superset of A such that the difference B\A is Ramsey-null. (c) 2006 Elsevier B.V. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	Annals of Pure and Applied Logic	en
dc.identifier.doi	10.1016/j.apal.2006.05.006	en
dc.identifier.isi	ISI:000240217700018	en
dc.identifier.volume	142	en
dc.identifier.issue	1-3	en
dc.identifier.spage	425	en
dc.identifier.epage	441	en