Forcing consequences of $\mathsc {PFA}$ together with the continuum large
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- by David Asperó and Miguel Angel Mota PDF
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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.References
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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
- 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).
- © Copyright 2015
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 3356931