1996/09/12 by Friedman, Sy D.
#FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.math/9609202
Assuming that ORD is ω+ω-Erdös we show that if a class forcing amenable to L (an L-forcing) has a generic then it has one definable in a set-generic extension of L[O^#]. In fact we may choose such a generic to be \it periodic in the sense that it preserve the indiscernibility of a final segment of a periodic subclass of the Silver indiscernibles, and therefore to be \it almost codable in the sense that it is definable from a real which is generic for an L-forcing (and which belongs to a set-generic extension of L[O^#]).