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4 Cards in this Set
- Front
- Back
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Axiom of Dependent Choices |
It states that if R is a binary relation on a nonempty set A and Dom(R) = A, then there existsan infinite sequence (a_n) such that (a_n,a_n+1) ∈ R for every n in ω. |
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constructible hierarchy: |
(a) L_0 = ∅. (b) For every α, L_α+1 consists of all definable subsets of Lα, that is,sets of the form {x ∈ L_α | P(x)}, where P is a formula of ZF withall quantified variables interpreted as ranging over Lα, and all freevariables other than x interpreted as particular elements of Lα. (c) If λ is a limit ordinal, then L_λ = Union from α<λ ( L_α) |
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Axiom of Constructibility |
The statement that everyset is constructible (formally, ∀x ∃α(x ∈ Lα)) is called the axiom ofconstructibility, written simply as V = L. We will write ZFL as anabbreviation for ZF + (V = L). |
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Relativization |
For any formula P of set theory, the relativization of Pto L, denoted P^L, means the formula P with every quantified variablerestricted to L. |
