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Forcing with ideals of closed sets

Jindrich Zapletal
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Abstract

Let I be a sigma-ideal sigma-generated by a projective collection of closed sets. The forcing with I-positive Borel sets is proper and adds a single real r of an almost minimal degree: if s is a real in V[r] then s is Cohen generic over V or V[s]=V[r].

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Jindrich Zapletal. 2001-09-04. Forcing with ideals of closed sets. https://arxiv.org/abs/math/0109026

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