# Conflict free colorings of (strongly) almost disjoint set-systems

Hajnal, Andras and Juhász, Istvan and Soukup, Lajos and Szentmiklossy, Zoltan (2010) Conflict free colorings of (strongly) almost disjoint set-systems. (Submitted)

 Preview
PDF
359Kb

## Abstract

is called a conflict free coloring of the set-system (with colors) if . The conflict free chromatic number of is the smallest for which admits a conflict free coloring with colors. is a -system if , for all , and is -almost disjoint, i.e. for distinct .
Our aim here is to study for , actually restricting ourselves to and . For instance, we prove that
for any limit cardinal (or ) and integers , GCH implies if , if ;
if then implies and implies ;
GCH implies for ,
V=L implies for ;
the existence of a supercompact cardinal implies the consistency of GCH plus and for ;
CH implies , while implies .

Item Type: Research Paper coloring, conflict-free coloring, almost disjoint, essentially disjoint 03E35 Consistency and independence results Research Divisions > Set theory and general topology 02 Apr 2010 11:16

Repository Staff Only: item control page