Projective maximal families of orthogonal measures with large continuum

الأصل · EN

We study maximal orthogonal families of Borel probability measures on 2ω (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 Σ¹₂-definable m.o. families and b=c=ω₃ (in fact any reasonable value of c will do). (2) There is a Δ¹₃-definable well order of the reals, there is a Π¹₂-definable m.o. family, there are no Σ¹₂-definable m.o. families, b=ω₁ and c=ω₂.