L Has A Reflection Principle
Proving that the axiom of separation, axiom of replacement, and axiom of choice hold in L requires (at least as shown above) the use of a reflection principle for L. Here we describe such a principle.
By mathematical induction on n<ω, we can use ZF in V to prove that for any ordinal α, there is an ordinal β>α such that for any sentence P(z1,...,zk) with z1,...,zk in Lβ and containing fewer than n symbols (counting a constant symbol for an element of Lβ as one symbol) we get that P(z1,...,zk) holds in Lβ if and only if it holds in L.
Read more about this topic: Constructible Universe
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