Abstract
Project # 34.8.2. Our first proof by transfinite induction. Suppose we are given an ordinal α and for all β <α the theorem is true, i.e., x ∈y ∈ V β implies x ∈ V β .Suppose x∈y∈ V α . You will need to separate the problem into cases:
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Case 1.
α = 0
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Case 2.
α = β +0 1 for some β, and
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Case 3.
α is a limit ordinal.
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© 1986 Springer-Verlag New York Inc.
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Henle, J.M. (1986). The Universe. In: An Outline of Set Theory. Problem Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8680-3_19
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DOI: https://doi.org/10.1007/978-1-4613-8680-3_19
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