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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Forcing consequences of $ PFA$ together with the continuum large


Authors: David Asperó and Miguel Angel Mota
Journal: Trans. Amer. Math. Soc. 367 (2015), 6103-6129
MSC (2010): Primary 03E50, 03E57, 03E35, 03E05
DOI: https://doi.org/10.1090/S0002-9947-2015-06205-9
Published electronically: February 13, 2015
MathSciNet review: 3356931
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Abstract: We develop a new method for building forcing iterations with symmetric systems of structures as side conditions. Using this method we prove that the forcing axiom for the class of all finitely proper posets of size $ \aleph _1$ is compatible with $ 2^{\aleph _{0}}> \aleph _2$. In particular, this answers a question of Moore by showing that $ \mho $ does not follow from this arithmetical assumption.


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Additional Information

David Asperó
Affiliation: School of Mathematics, University of East Anglia, Norwich NR4 7TJ, United Kingdom
Email: d.aspero@uea.ac.uk

Miguel Angel Mota
Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 2E4
Email: motagaytan@gmail.com

DOI: https://doi.org/10.1090/S0002-9947-2015-06205-9
Received by editor(s): October 4, 2011
Received by editor(s) in revised form: May 31, 2013
Published electronically: February 13, 2015
Additional Notes: The second author was supported by the Austrian Science Fund FWF Project P22430. Both authors were also partially supported by Ministerio de Educación y Ciencia Project MTM2008–03389 (Spain) and by Generalitat de Catalunya Project 2009SGR–00187 (Catalonia).
Article copyright: © Copyright 2015 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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