Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strong partition relations below the power set: consistency, was
  Sierpinski right, II?   We continue here [Sh276] but we do not relay on it. The motivation was a
conjecture of Galvin stating that 2^{omega} >= omega_2 + omega_2->
[omega_1]^{n}_{h(n)} is consistent for a suitable h: omega-> omega. In section
5 we disprove this and give similar negative results. In section 3 we prove the
consistency of the conjecture replacing omega_2 by 2^omega, which is quite
large, starting with an Erd\H{o}s cardinal. In section 1 we present iteration
lemmas which are needed when we replace omega by a larger lambda and in section
4 we generalize a theorem of Halpern and Lauchli replacing omega by a larger
lambda .

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The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
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The categories of this paper are: cs
10
The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci