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  1.  12
    Comparisons of polychromatic and monochromatic Ramsey theory.Justin Palumbo - 2013 - Journal of Symbolic Logic 78 (3):951-968.
  2.  19
    Unbounded and dominating reals in Hechler extensions.Justin Palumbo - 2013 - Journal of Symbolic Logic 78 (1):275-289.
    We give results exploring the relationship between dominating and unbounded reals in Hechler extensions, as well as the relationships among the extensions themselves. We show that in the standard Hechler extension there is an unbounded real which is dominated by every dominating real, but that this fails to hold in the tree Hechler extension. We prove a representation theorem for dominating reals in the standard Hechler extension: every dominating real eventually dominates a sandwich composition of the Hechler real with two (...)
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  3.  61
    The rigid relation principle, a new weak choice principle.Joel David Hamkins & Justin Palumbo - 2012 - Mathematical Logic Quarterly 58 (6):394-398.
    The rigid relation principle, introduced in this article, asserts that every set admits a rigid binary relation. This follows from the axiom of choice, because well-orders are rigid, but we prove that it is neither equivalent to the axiom of choice nor provable in Zermelo-Fraenkel set theory without the axiom of choice. Thus, it is a new weak choice principle. Nevertheless, the restriction of the principle to sets of reals is provable without the axiom of choice.
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