Abstract
As an application of the general theory development in the previous sections we give a definition of “forcing” and derive its elementary properties. Throughout this section, M denotes a standard transitive model of ZF, P ∈ M is a partial order structure, and B is the corresponding M-complete Boolean algebra of regular open sets of P in the relative sense of M. Further-more we have
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h an M-complete homomorphism of B into 2,
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F an M-complete ultrafilter for B, and
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G a set that is P-generic over M,
Such that h, F, and G are related to each as described in §2. Thus one of them may be given and the remaining sets are obtained from it as in §2.
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© 1973 Springer-Verlag New York Inc.
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Takeuti, G., Zaring, W.M. (1973). Forcing. In: Axiomatic Set Theory. Graduate Texts in Mathematics, vol 8. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-8751-0_11
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DOI: https://doi.org/10.1007/978-1-4684-8751-0_11
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90050-6
Online ISBN: 978-1-4684-8751-0
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