English

Projective maximal families of orthogonal measures with large continuum

Logic 2011-06-22 v1

Abstract

We study maximal orthogonal families of Borel probability measures on 2ω2^\omega (abbreviated m.o. families) and show that there are generic extensions of the constructible universe LL in which each of the following holds: (1) There is a Δ31\Delta^1_3-definable well order of the reals, there is a Π21\Pi^1_2-definable m.o. family, there are no Σ21\mathbf{\Sigma}^1_2-definable m.o. families and b=c=ω3\mathfrak{b}=\mathfrak{c}=\omega_3 (in fact any reasonable value of c\mathfrak{c} will do). (2) There is a Δ31\Delta^1_3-definable well order of the reals, there is a Π21\Pi^1_2-definable m.o. family, there are no Σ21\mathbf{\Sigma}^1_2-definable m.o. families, b=ω1\mathfrak{b}=\omega_1 and c=ω2\mathfrak{c}=\omega_2.

Keywords

Cite

@article{arxiv.1106.4273,
  title  = {Projective maximal families of orthogonal measures with large continuum},
  author = {Vera Fischer and Sy-David Friedman and Asger Tornquist},
  journal= {arXiv preprint arXiv:1106.4273},
  year   = {2011}
}

Comments

12 pages