Projective maximal families of orthogonal measures with large continuum

2011/06/21 by Vera Fischer, Fischer, Vera, Sy‐David Friedman +5
Computer Science · Mathematics · #03E15 #03E17 #03E35 #03E45 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis #math.LO #msc:03E15 #msc:03E17 #msc:03E35 #msc:03E45

paper · pdf · doi:10.48550/arxiv.1106.4273

12 pages

arxiv created 2011/06/21 · openalex publication_date 2011/06/21 · arxiv updated 2011/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study maximal orthogonal families of Borel probability measures on 2^ω (abbreviated m.o. families) and show that there are generic extensions of the constructible universe L in which each of the following holds: (1) There is a Δ¹₃-definable well order of the reals, there is a Π¹₂-definable m.o. family, there are no \mathbfΣ¹₂-definable m.o. families and \mathfrakb=\mathfrakc=ω₃ (in fact any reasonable value of \mathfrakc will do). (2) There is a Δ¹₃-definable well order of the reals, there is a Π¹₂-definable m.o. family, there are no \mathbfΣ¹₂-definable m.o. families, \mathfrakb=ω₁ and \mathfrakc=ω₂.

Related

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• Good projective witnesses
• A co-analytic maximal set of orthogonal measures
• Orthogonal Families of Real Sequences
• Extreme points of a ball about a measure with finite support