Projective maximal families of orthogonal measures with large continuum

Details Projective maximal families of orthogonal measures with large continuum Projective maximal families of orthogonal measures with large continuum

2011-06-21

arxiv.org/abs/1106.4273v1

Mathematics

Logic

12 pages

Scientific paper

We study maximal orthogonal families of Borel probability measures on $2^\omega$ (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 $\Delta^1_3$-definable well order of the reals, there is a $\Pi^1_2$-definable m.o. family, there are no $\mathbf{\Sigma}^1_2$-definable m.o. families and $\mathfrak{b}=\mathfrak{c}=\omega_3$ (in fact any reasonable value of $\mathfrak{c}$ will do). (2) There is a $\Delta^1_3$-definable well order of the reals, there is a $\Pi^1_2$-definable m.o. family, there are no $\mathbf{\Sigma}^1_2$-definable m.o. families, $\mathfrak{b}=\omega_1$ and $\mathfrak{c}=\omega_2$.

Affiliated with

Also associated with

No associations

Rating

Projective maximal families of orthogonal measures with large continuum does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Projective maximal families of orthogonal measures with large continuum, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Projective maximal families of orthogonal measures with large continuum will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-179511