Forcing consequences of PFA together with the continuum large

David Aspero; Miguel Angel Mota

doi:10.1090/S0002-9947-2015-06205-9

Forcing consequences of PFA together with the continuum large

David Aspero, Miguel Angel Mota

Logic

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14 Citations (Scopus)

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Abstract

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 language	English
Pages (from-to)	6103-6129
Journal	Transactions of the American Mathematical Society
Volume	367
Issue number	9
Early online date	13 Feb 2015
DOIs	https://doi.org/10.1090/S0002-9947-2015-06205-9
Publication status	Published - Sep 2015

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10.1090/S0002-9947-2015-06205-9

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David Aspero
- D.Asperouea.acuk
- School of Engineering, Mathematics and Physics - Associate Professor in Pure Mathematics
- Logic - Member
Person: Research Group Member, Academic, Teaching & Research

Cite this

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AB - 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.

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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

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Forcing consequences of PFA together with the continuum large

Abstract

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David Aspero

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