2007/09/19 by Piotr Kalemba, Kalemba, Piotr, Szymon Plewik +3
Mathematics · #Commutative Algebra and Its Applications #Rings, Modules, and Algebras #math.CO #math.GN #math.LO #msc:03E35 #msc:03E50 #msc:26A03 #msc:28A05 #msc:54A10
paper · pdf · doi:10.48550/arxiv.0709.3016
Accepted for publication in CEJM
arxiv created 2008/03/03 · arxiv updated 2009/12/01
The σ-ideal (v0) is associated with the Silver forcing, see \citebre. Also, it constitutes the family of all completely doughnut null sets, see \citehal. We introduce segments and *-segments topologies, to state some resemblances of (v0) to the family of Ramsey null sets. To describe add(v0) we adopt a proof of Base Matrix Lemma. Consistent results are stated, too. Halbeisen's conjecture cov(v0) = add(v0) is confirmed under the hypothesis t= min \\cf (\frak c), r\ . The hypothesis h=ω1 implies that (v0) has the ideal type (\frak c, ω1,\frak c).