Forcing consequences of PFA together with the continuum large

David Aspero, Miguel Angel Mota

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We develop a new method for building forcing iterations with symmetric systems of structures as side conditions. Using our method we prove that the forcing axiom for the class of all the finitely proper posets of small size is compatible with the continuum being larger than the second uncountable cardinal . In particular, this answers a question of Justin Moore by showing that ? does not follow from this arithmetical assumption.
Original languageEnglish
Pages (from-to)6103-6129
JournalTransactions of the American Mathematical Society
Issue number9
Early online date13 Feb 2015
Publication statusPublished - Sep 2015

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