Dependent choice, properness, and generic absoluteness

Aspero, David and Karagila, Asaf (2020) Dependent choice, properness, and generic absoluteness. The Review of Symbolic Logic, 14 (1). 225–249. ISSN 1755-0203

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Abstract

We show that Dependent Choice is a sufficient choice principle for developing the basic theory of proper forcing, and for deriving generic absoluteness for the Chang model in the presence of large cardinals, even with respect to -preserving symmetric submodels of forcing extensions. Hence, not only provides the right framework for developing classical analysis, but is also the right base theory over which to safeguard truth in analysis from the independence phenomenon in the presence of large cardinals. We also investigate some basic consequences of the Proper Forcing Axiom in, and formulate a natural question about the generic absoluteness of the Proper Forcing Axiom in and. Our results confirm as a natural foundation for a significant portion of classical mathematics and provide support to the idea of this theory being also a natural foundation for a large part of set theory.

Item Type: Article
Uncontrolled Keywords: axiom of choice,pfa,the chang model,forcing axioms,generic absoluteness,proper forcing,the chang model,logic,philosophy,mathematics (miscellaneous) ,/dk/atira/pure/subjectarea/asjc/2600/2609
Faculty \ School: Faculty of Science > School of Mathematics
Related URLs:
Depositing User: LivePure Connector
Date Deposited: 03 Apr 2020 00:41
Last Modified: 05 Nov 2021 01:37
URI: https://ueaeprints.uea.ac.uk/id/eprint/74693
DOI: 10.1017/S1755020320000143

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