Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Indestructible colourings and rainbow Ramsey theorems   We give a negative answer to a question of Erdos and Hajnal: it is consistent
that GCH holds and there is a colouring $c:[{\omega_2}]^2\to 2$ establishing
$\omega_2 \not\to [(\omega_1;{\omega})]^2_2$ such that some colouring
$g:[\omega_1]^2\to 2$ can not be embedded into $c$. It is also consistent that
$2^{\omega_1}$ is arbitrarily large, and a function $g$ establishes
$2^{\omega_1} \not\to [(\omega_1,\omega_2)]^2_{\omega_1}$ such that there is no
uncountable $g$-rainbow subset of $2^{\omega_1}$. We also show that for each
$k\in {\omega}$ it is consistent with Martin's Axiom that the negative
partition relation $\omega_1 \not\to^* [(\omega_1;\omega_1)]_{k-bdd}$ holds.

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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org