The polarized Ramsey’s theorem

Archive for Mathematical Logic 48 (2):141-157 (2009)

Abstract
We study the effective and proof-theoretic content of the polarized Ramsey’s theorem, a variant of Ramsey’s theorem obtained by relaxing the definition of homogeneous set. Our investigation yields a new characterization of Ramsey’s theorem in all exponents, and produces several combinatorial principles which, modulo bounding for ${\Sigma^0_2}$ formulas, lie (possibly not strictly) between Ramsey’s theorem for pairs and the stable Ramsey’s theorem for pairs
Keywords Mathematics   Algebra   Mathematics, general   Mathematical Logic and Foundations
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DOI 10.1007/s00153-008-0108-0
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References found in this work BETA

Subsystems of Second-Order Arithmetic.Stephen G. Simpson - 2004 - Studia Logica 77 (1):129-129.
On the Strength of Ramsey's Theorem.David Seetapun & Theodore A. Slaman - 1995 - Notre Dame Journal of Formal Logic 36 (4):570-582.

View all 10 references / Add more references

Citations of this work BETA

Open Questions in Reverse Mathematics.Antonio Montalbán - 2011 - Bulletin of Symbolic Logic 17 (3):431-454.
Reverse Mathematics: The Playground of Logic.Richard A. Shore - 2010 - Bulletin of Symbolic Logic 16 (3):378-402.
Partitions of Trees and $${{\Sf ACA}^\Prime_{0}}$$.Bernard A. Anderson & Jeffry L. Hirst - 2009 - Archive for Mathematical Logic 48 (3-4):227-230.

View all 7 citations / Add more citations

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