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The Proper Forcing Axiom, Prikry forcing, and the Singular Cardinals Hypothesis

✍ Scribed by Justin Tatch Moore

Publisher
Elsevier Science
Year
2006
Tongue
English
Weight
156 KB
Volume
140
Category
Article
ISSN
0168-0072

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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 βˆ‘~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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## Abstract We introduce a new simple way of defining the forcing method that works well in the usual setting under FA, the Foundation Axiom, and moreover works even under Aczel's AFA, the Anti‐Foundation Axiom. This new way allows us to have an intuition about what happens in defining the forcing

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## Abstract A note on the effects of a weak discontinuity in the forcing function __g(x)__ of a singular, integral equation of the first kind and the resulting strong discontinuity that can appear in the solution __f__(__x__) is presented.