Techniques for approaching the dual Ramsey property in the projective hierarchy

2001/09/23 by Lorenz Halbeisen, Benedikt Loewe
Mathematics · #math.LO #msc:03E15 #msc:03E40 #msc:03E05 #msc:05A18 #msc:05D10 #msc:03E60

paper · pdf

published as Pacific Journal of Mathematics 200(1) (2001) 119-145

arxiv created 2001/09/23 · arxiv updated 2009/11/30

Abstract

We define the dualizations of objects and concepts which are essential for investigating the Ramsey property in the first levels of the projective hierarchy, prove a forcing equivalence theorem for dual Mathias forcing and dual Laver forcing, and show that the Harrington-Kechris techniques for proving the Ramsey property from determinacy work in the dualized case as well.

Related

• Symmetries between two Ramsey properties
• Forcing in Ramsey theory
• Box Ramsey and Canonical Colourings
• Ramsey theory over partitions I: Positive Ramsey relations from forcing axioms
• Controlling iterated jumps of solutions to combinatorial problems