Non-cohen oracle C.C.C.

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 satis es it. We generalize this to other cases. In Section 1 we replace Cohen by "nicely " de nable 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.