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Logic and foundations the proper forcing axiom. (English) Zbl 1258.03075

Bhatia, Rajendra (ed.) et al., Proceedings of the international congress of mathematicians (ICM 2010), Hyderabad, India, August 19–27, 2010. Vol. II: Invited lectures. Hackensack, NJ: World Scientific; New Delhi: Hindustan Book Agency (ISBN 978-981-4324-32-8/hbk; 978-81-85931-08-3/hbk; 978-981-4324-30-4/set; 978-981-4324-35-9/ebook). 3-29 (2011).
This is a well-written, albeit somewhat terse, survey of applications of the Proper Forcing Axiom. It covers some of the more ‘modern’ applications of this principle, such as the Open Colouring Axiom and the P-ideal dichotomy; these themselves have become useful principles in their own right, as the author demonstrates. The survey is terse in that for a full appreciation of the many results the reader will have to consult the original sources. Nevertheless, with the generous list of references this paper is a good place to start exploring PFA.
For the entire collection see [Zbl 1220.00032].
Reviewer: K. P. Hart (Delft)

MSC:

03E57 Generic absoluteness and forcing axioms
03E35 Consistency and independence results
03E55 Large cardinals
03E75 Applications of set theory
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