2016/10/09 by HAIM HOROWITZ, Horowitz, Haim, SAHARON SHELAH +1
#FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1610.02706
Using creature technology, we construct families of Suslin ccc non-sweet forcing notions \mathbb Q such that ZFC is equiconsistent with ZF+"every set of reals equals a Borel set modulo the (≤ ℵ1)-closure of the null ideal associated with \mathbb Q"+"there is an ω1-sequence of distinct reals". This answers a question of the second author and Kellner. As an application of independent interest, we also show how our forcing adds a new Π12 singleton over L without relying on L-combinatorics.