We present a method to iterate finitely splitting lim-sup tree forcings along non-wellfounded linear orders. As an application, we introduce a new method to force (weak) measurability of all definable sets with respect to a certain (non-ccc) ideal.
"Saccharinity." J. Symbolic Logic 76 (4) 1153 - 1183, December 2011. https://doi.org/10.2178/jsl/1318338844