Hindman's theorem: an ultrafilter argument in second order arithmetic

Hindman's theorem: an ultrafilter argument in second order arithmetic. Towsner, H. J. Symbolic Logic, 76(1):353–360, 2011.

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Hindman's Theorem is a prototypical example of a combinatorial theorem with a proof that uses the topology of the ultrafilters. We show how the methods of this proof, including topological arguments about ultrafilters, can be translated into second order arithmetic.

@article {MR2791353,
    AUTHOR = {Towsner, Henry},
     TITLE = {Hindman's theorem: an ultrafilter argument in second order
              arithmetic},
   JOURNAL = {J. Symbolic Logic},
  FJOURNAL = {Journal of Symbolic Logic},
    VOLUME = {76},
      YEAR = {2011},
    NUMBER = {1},
     PAGES = {353--360},
      ISSN = {0022-4812},
     CODEN = {JSYLA6},
   MRCLASS = {03F35 (54D80)},
  MRNUMBER = {2791353 (2012b:03165)},
MRREVIEWER = {M. Yasuhara},
       DOI = {10.2178/jsl/1294171005},
       URLJOURNAL= {http://dx.doi.org/10.2178/jsl/1294171005},
urlarxiv={http://arxiv.org/abs/0906.3882},
abstract={Hindman's Theorem is a prototypical example of a combinatorial theorem with a proof that uses the topology of the ultrafilters. We show how the methods of this proof, including topological arguments about ultrafilters, can be translated into second order arithmetic.},
}

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