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math.LO2012
Comparisons of polychromatic and monochromatic Ramsey theory
Justin Palumbo
We compare the strength of polychromatic and monochromatic Ramsey theory in several set-theoretic domains. We show that the rainbow Ramsey theorem does not follow from ZF, nor does…
math.LO2012
Unbounded and dominating reals in Hechler extensions
Justin Palumbo
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…
math.LO2011
The Rigid Relation Principle, a New Weak Choice Principle
Joel David Hamkins, Justin Palumbo
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 rigi…