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Abstract  

It is consistent that there exists an uncountably chromatic triple system which does not contain two triples with two common points or circuits of lengths 3, 5.

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Abstract

If is a system of infinite sets, |AB|<r for (r<ω) then has a conflict free coloring with ω colors, i.e., a function so that each has a color i<ω with |F −1(i)∩A|=1.

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Abstract

We prove the consistency of a singular cardinal λ with small value of the ultrafilter number , and arbitrarily large value of 2λ.

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Abstract  

We determine a class of triple systems such that each must occur in a triple system with uncountable chromatic number that omits
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(the unique system consisting of two triples on four vertices). This class contains all odd circuits of length ≧ 7. We also show that consistently there are two finite triple systems such that they can separately be omitted by uncountably chromatic triple systems but not both.
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Acta Mathematica Hungarica
Authors: András Hajnal, István Juhász, Lajos Soukup, and Zoltán Szentmiklóssy

Abstract

is called a conflict free coloring of the set-system (with ρ colors) if
ea
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
eb
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
ec

• if λκω>d>1, then λ<κ +ω implies and λ≧ℶω(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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Abstract  

We investigate the chromatic number of infinite graphs whose definition is motivated by the theorem of Engelking and Karłowicz (in [?]). In these graphs, the vertices are subsets of an ordinal, and two subsets X and Y are connected iff for some aXY the order-type of aX is different from that of aY. In addition to the chromatic number x(G) of these graphs we study χκ(G), the κ-chromatic number, which is the least cardinal µ with a decomposition of the vertices into µ classes none of which contains a κ-complete subgraph.

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Abstract  

We prove that the cardinal estimates given by Shelah’s bound on the Galvin-Hajnal norm can be obtained via PCF topology alone.

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János Gerlits died unexpectedly in 2008. In this paper we attempt to make a small tribute to his very powerful mathematical legacy by describing the emerging impact of two ideas, γ-spaces and Gerlits-Nagy spaces, from [19] and [20].

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.0451) (0.0451) (0.0451) (0.0451) (0.0450) Age –2.03e05 3.64e−05 2.28e−05 2.50e−05 –6.82e−05 –2.46e−05 (0.000993) (0.000994) (0.000992) (0.000994) (0.000994) (0.000994) Volatility 9.53e−05 8.78e−05 8.36e−05 8.82e−05 9.32e−05 8.07e−05 (0.000267) (0

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