Iterating Symmetric Extensions

Karagila, Asaf (2019) Iterating Symmetric Extensions. Journal of Symbolic Logic, 84 (1). 123–159. ISSN 0022-4812

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Abstract

The notion of a symmetric extension extends the usual notion of forcing by identifying a particular class of names which forms an intermediate model of  between the ground model and the generic extension, and often the axiom of choice fails in these models. Symmetric extensions are generally used to prove choiceless consistency results. We develop a framework for iterating symmetric extensions in order to construct new models of  . We show how to obtain some well-known and lesser-known results using this framework. Specifically, we discuss Kinna–Wagner principles and obtain some results related to their failure.

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: LivePure Connector
Date Deposited: 29 Mar 2019 11:30
Last Modified: 13 Oct 2019 00:45
URI: https://ueaeprints.uea.ac.uk/id/eprint/70372
DOI: 10.1017/jsl.2018.73

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