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Acta Mathematica Hungarica
András Hajnal
István Juhász
Lajos Soukup
, and
Zoltán Szentmiklóssy


is called a conflict free coloring of the set-system (with ρ colors) if
The conflict free chromatic number of is the smallest ρ for which admits a conflict free coloring with ρ colors.
is a (λ,κ,μ)-system if , |A|=κ for all , and is μ-almost disjoint, i.e. |AA′|<μ for distinct . Our aim here is to study
for λκμ, actually restricting ourselves to λω and μω.

For instance, we prove that

• for any limit cardinal κ (or κ=ω) and integers n≧0, k>0, GCH implies

• if λκω>d>1, then λ<κ +ω implies and λ≧ℶ ω (κ) implies ;

• GCH implies for λκω 2 and V=L implies for λκω 1;

• the existence of a supercompact cardinal implies the consistency of GCH plus and for 2≦nω;

• CH implies , while implies .

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