Hechler and Laver Trees

Details Hechler and Laver Trees Hechler and Laver Trees

2012-04-23

arxiv.org/abs/1204.5198v1

Mathematics

Logic

Scientific paper

A Laver tree is a tree in which each node splits infinitely often. A Hechler tree is a tree in which each node splits cofinitely often. We show that every analytic set is either disjoint from the branches of a Heckler tree or contains the branches of a Laver tree. As a corollary we deduce Silver Theorem that all analytic sets are Ramsey. We show that in Godel's constructible universe that our result is false for co-analytic sets (equivalently it fails for analytic sets if we switch Hechler and Laver). We show that under Martin's axiom that our result holds for Sigma^1_2 sets. Finally we define two games related to this property. Latex2e 8 pages Latest version at http://www.math.wisc.edu/~miller/res/index.html

Affiliated with

Also associated with

No associations

Rating

Hechler and Laver Trees 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 Hechler and Laver Trees, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hechler and Laver Trees will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-518367