ITERATING SYMMETRIC EXTENSIONS
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AbstractThe notion of a symmetric extension extends the usual notion of forcing by identifying a particular class of names which forms an intermediate model of $ZF$ 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 $ZF$. 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.
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2020 ◽
Vol 476
(2239)
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pp. 20190782
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2003 ◽
Vol 68
(4)
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pp. 1091-1108
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