Abstract
Forcing is a technique—invented by Cohen in the early 1960s—for proving the independence, or at least the consistency, of certain statements relative to ZFC. In fact, starting from a model of ZFC, Cohen constructed in 1962 models of ZF in which the Axiom of Choice fails as well as models of ZFC in which the Continuum Hypothesis fails. On the other hand, starting from a model of ZF, Gödel constructed a model of ZFC in which the Continuum Hypothesis holds (cf. Chapter 5). By combining these results we find that the Axiom of Choice is independent of ZF and that the Continuum Hypothesis is independent of ZFC.
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© 2012 Springer-Verlag London Limited
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Halbeisen, L.J. (2012). The Idea of Forcing. In: Combinatorial Set Theory. Springer Monographs in Mathematics. Springer, London. https://doi.org/10.1007/978-1-4471-2173-2_12
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DOI: https://doi.org/10.1007/978-1-4471-2173-2_12
Publisher Name: Springer, London
Print ISBN: 978-1-4471-2172-5
Online ISBN: 978-1-4471-2173-2
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