# Sh:669

• Shelah, S. (2006). Non-Cohen oracle C.C.C. J. Appl. Anal., 12(1), 1–17.
• Abstract:
The oracle c.c.c. is closed related to Cohen forcing. During an iteration we can “omit a type”; i.e. preserve “the intersection of a given family of Borel sets of reals is empty” provided that Cohen forcing satisfies it. We generalize this to other cases. In §1 we replace Cohen by “nicely” definable c.c.c., do the parallel of the oracle c.c.c. and end with a criterion for extracting a subforcing (not a complete subforcing) of a given nicely one and satisfying the oracle.
• Current version: 2011-11-07_10 (29p) published version (17p)
Bib entry
@article{Sh:669,
author = {Shelah, Saharon},
title = {{Non-Cohen oracle C.C.C}},
journal = {J. Appl. Anal.},
fjournal = {Journal of Applied Analysis},
volume = {12},
number = {1},
year = {2006},
pages = {1--17},
issn = {1425-6908},
doi = {10.1515/JAA.2006.1},
mrclass = {03E35 (03E17)},
mrnumber = {2243849},
mrreviewer = {Juris Stepr\=ans},
doi = {10.1515/JAA.2006.1},
note = {\href{https://arxiv.org/abs/math/0303294}{arXiv: math/0303294}},
arxiv_number = {math/0303294}
}