Mathematics – Logic
Scientific paper
1995-08-23
Mathematics
Logic
Scientific paper
We prove that if $\bI$ is a p.\ o. set in a countable transitive model $\gM$ of $\ZFC$ then $\gM$ can be extended by a generic sequence of reals $\a_\i,$ $\i\in\bI,$ such that $\aleph_1^\gM$ is preserved and every $\a_\i$ is Sacks generic over $\gM[\ang{\a_\j:\j<\i}]$. The structure of the degrees of \dd\gM constructibility of reals in the extension is investigated. As an application, we obtain a model in which the $\is12$ equivalence relation $x \E y$ iff $\rL[x]=\rL[y]$ ($x,\,y$ are reals) does not admit a reasonable form of the Glimm -- Effros theorem.
No associations
LandOfFree
On nonwellfounded iterated Sacks extensions, with application to the Glimm -- Effros property 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 On nonwellfounded iterated Sacks extensions, with application to the Glimm -- Effros property, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On nonwellfounded iterated Sacks extensions, with application to the Glimm -- Effros property will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-710231