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
Famous quotes containing the words reflection and/or principle:
“If the contemplation, even of inanimate beauty, is so delightful; if it ravishes the senses, even when the fair form is foreign to us: What must be the effects of moral beauty? And what influence must it have, when it embellishes our own mind, and is the result of our own reflection and industry?”
—David Hume (1711–1776)
“There is a good principle which created order, light, and man, and an evil principle which created chaos, darkness, and woman.”
—Pythagoras (c. 572–497 B.C.)