Abstract
The methods applied in the previous chapters are classical and, in a certain sense, elementary. In this chapter, we will introduce modern model theoretic methods. Notions such as “model of ZFC” and “absoluteness of a formula” are introduced. For any infinite cardinal number Θ we define the set H(Θ) of those sets which are hereditarily of cardinality less than Θ. We will show that for all regular uncountable cardinals Θ, H(Θ) is a model of all axioms of ZFC except the power set axiom.
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© 1999 Springer Basel AG
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Holz, M., Steffens, K., Weitz, E. (1999). Approximation Sequences. In: Introduction to Cardinal Arithmetic. Modern Birkhäuser Classics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0346-0330-0_5
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DOI: https://doi.org/10.1007/978-3-0346-0330-0_5
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0346-0327-0
Online ISBN: 978-3-0346-0330-0
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