On effective sigma-boundedness and sigma-compactness

Details On effective sigma-boundedness and sigma-compactness On effective sigma-boundedness and sigma-compactness

2011-10-05

arxiv.org/abs/1110.0919v1

Mathematics

Logic

arXiv admin note: substantial text overlap with arXiv:1103.1060

Scientific paper

We prove several theorems on sigma-bounded and sigma-compact pointsets. We start with a known theorem by Kechris, saying that any lightface \Sigma^1_1 set of the Baire space either is effectively sigma-bounded (that is, covered by a countable union of compact lightface \Delta^1_1 sets), or contains a superperfect subset (and then the set is not sigma-bounded, of course). We add different generalizations of this result, in particular, 1) such that the boundedness property involved includes covering by compact sets and equivalence classes of a given finite collection of lightface \Delta^1_1 equivalence relations, 2) generalizations to lightface \Sigma^1_2 sets, 3) generalizations true in the Solovay model. As for effective sigma-compactness, we start with a theorem by Louveau, saying that any lightface \Delta^1_1 set of the Baire space either is effectively sigma-compact (that is, is equal to a countable union of compact lightface \Delta^1_1 sets), or it contains a relatively closed superperfect subset. Then we prove a generalization of this result to lightface \Sigma^1_1 sets.

Affiliated with

Also associated with

No associations

Rating

On effective sigma-boundedness and sigma-compactness does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On effective sigma-boundedness and sigma-compactness, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On effective sigma-boundedness and sigma-compactness will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-324731