Most Downloaded Articles
- Common fixed points of nonexpansive mappings with applications to best and best simultaneous approximation by Chandok, Sumit and Narang, T. D.
- Regularity theory for superquadratic energy functionals related to nonlinear Hencky materials in three dimensions by Breit, Dominic
- Projective coordinates and compactification in elliptic, parabolic and hyperbolic 2-D geometry by Biswas, Debapriya
- The generalized Stokes theorem for ℝ-linear forms on Lie algebroids by Balcerzak, Bogdan
Non-Cohen Oracle C.C.C.
1The Hebrew University of Jerusalem, Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, Jerusalem 91904, Israel. e-mail: (email)
2Department of Mathematics, Hill Center — Busch Campus, Rutgers, The State University of New Jersey, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019, USA
Citation Information: Journal of Applied Analysis. Volume 12, Issue 1, Pages 1–17, ISSN (Online) 1869-6082, ISSN (Print) 1425-6908, DOI: 10.1515/JAA.2006.1, June 2010
- Published Online:
The oracle c.c.c. is closely 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 Section 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.