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Forcing axiom failure for any lambda>aleph_1

Saharon Shelah
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Abstract

David Aspero asks on the possibility of having Forcing axiom FA_{aleph_2}(K), where K is the class of forcing notions preserving stationarity of subsets of aleph_1 and of aleph_2. We answer negatively, in fact we show the negative result for any regular lambda>aleph_1 even demanding adding no new sequence of ordinals of length<lambda.

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Saharon Shelah. 2001-12-27. Forcing axiom failure for any lambda>aleph_1. https://arxiv.org/abs/math/0112286

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