Mathematics – Logic
Scientific paper
2010-01-16
Mathematics
Logic
Scientific paper
With every $\sigma$-ideal $I$ on a Polish space we associate the $\sigma$-ideal $I^*$ generated by the closed sets in $I$. We study the forcing notions of Borel sets modulo the respective $\sigma$-ideals $I$ and $I^*$ and find connections between their forcing properties. To this end, we associate to a $\sigma$-ideal on a Polish space an ideal on a countable set and show how forcing properties of the forcing depend on combinatorial properties of the ideal. For $\sigma$-ideals generated by closed sets we also study the degrees of reals added in the forcing extensions. Among corollaries of our results, we get necessary and sufficient conditions for a $\sigma$-ideal $I$ generated by closed sets, under which every Borel function can be restricted to an $I$-positive Borel set on which it is either 1-1 or constant.
Sabok Marcin
Zapletal Jindřich
No associations
LandOfFree
Forcing properties of ideals of closed sets 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 Forcing properties of ideals of closed sets, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Forcing properties of ideals of closed sets will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-88366