Journal of Mathematical Logic 9 (2):159-165 (2009)
AbstractThe Filter Dichotomy says that every uniform nonmeager filter on the integers is mapped by a finite-to-one function to an ultrafilter. The consistency of this principle was proved by Blass and Laflamme. A medial limit is a universally measurable function from [Formula: see text] to the unit interval [0, 1] which is finitely additive for disjoint sets, and maps singletons to 0 and ω to 1. Christensen and Mokobodzki independently showed that the Continuum Hypothesis implies the existence of medial limits. We show that the Filter Dichotomy implies that there are no medial limits.
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References found in this work
There May Be Simple Pℵ1 and Pℵ2-Points and the Rudin-Keisler Ordering May Be Downward Directed.Andreas Blass & Saharon Shelah - 1987 - Annals of Pure and Applied Logic 33 (3):213-243.
Countable Borel Equivalence Relations.S. Jackson, A. S. Kechris & A. Louveau - 2002 - Journal of Mathematical Logic 2 (01):1-80.
Consistency Results About Filters and the Number of Inequivalent Growth Types.Andreas Blass & Claude Laflamme - 1989 - Journal of Symbolic Logic 54 (1):50-56.
Amenable Equivalence Relations and Turing Degrees.Alexander S. Kechris - 1991 - Journal of Symbolic Logic 56 (1):182-194.
Near Coherence of Filters. III. A Simplified Consistency Proof.Andreas Blass & Saharon Shelah - 1989 - Notre Dame Journal of Formal Logic 30 (4):530-538.
Citations of this work
Tools, Objects, and Chimeras: Connes on the Role of Hyperreals in Mathematics.Vladimir Kanovei, Mikhail G. Katz & Thomas Mormann - 2013 - Foundations of Science 18 (2):259-296.
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