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Bounded forcing axioms and the continuum

✍ Scribed by David Asperó; Joan Bagaria

Book ID
104307091
Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
241 KB
Volume
109
Category
Article
ISSN
0168-0072

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✦ Synopsis

We show that bounded forcing axioms (for instance, the Bounded Proper Forcing Axiom and the Bounded Semiproper Forcing Axiom) are consistent with the existence of (!2; !2)-gaps and thus do not imply the Open Coloring Axiom. They are also consistent with Jensen's combinatorial principles for L at the level !2, and therefore with the existence of an !2-Suslin tree. We also show that the axiom we call BMM ℵ 3 implies ℵ ℵ 1 2 =ℵ2, as well as a stationary re ection principle which has many of the consequences of Martin's Maximum for objects of size ℵ2. Finally, we give an example of a so-called boldface bounded forcing axiom implying 2 ℵ 0 = ℵ2.

📜 SIMILAR VOLUMES

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## Abstract We introduce the Bounded Axiom A Forcing Axiom (BAAFA). It turns out that it is equiconsistent with the existence of a regular ∑~2~‐correct cardinal and hence also equiconsistent with BPFA. Furthermore we show that, if consistent, it does not imply the Bounded Proper Forcing Axiom (BPFA

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