## Saccharinity.(English)Zbl 1247.03109

Summary: 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.

### MSC:

 3e+35 Consistency and independence results 3e+40 Other aspects of forcing and Boolean-valued models
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### References:

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