Preserving Non-Null with Suslin+ forcing

Details Preserving Non-Null with Suslin+ forcing Preserving Non-Null with Suslin+ forcing

2002-11-25

arxiv.org/abs/math/0211385v3

Arch. Math. Logic 45 (2006), no. 6, 649 -- 664

Mathematics

Logic

14 pages

Scientific paper

10.1007/s00153-006-0008-0

We introduce the notion of effective Axiom A and use it to show that some popular tree forcings are Suslin+. We introduce transitive nep and present a simplified version of Shelah's "preserving a little implies preserving much": If I is a Suslin ccc ideal (e.g. Lebesgue-null or meager) and P is a transitive nep forcing (e.g. P is Suslin+) and P doesn't make any I-positive Borel set small, then P doesn't make any I-positive set small.

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