Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Erdos-Moser and ISigma_2   The first-order part of the Ramsey's Theorem for pairs with an arbitrary
number of colors is known to be precisely BSigma03. We compare this to the
known division of Ramsey's Theorem for pairs into the weaker principles, EM
(the Erd\H{o}s-Moser principle) and ADS (the ascending-descending sequence
principle): we show that the additional strength beyond ISigma02 is entirely
due to the arbitrary color analog of ADS.
  Specifically, we show that ADS for an arbitrary number of colors implies
BSigma03 while EM for an arbitrary number of colors is Pi11-conservative over
ISigma02 and it does not imply ISigma02.

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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat