In set theory, a branch of mathematics, a reflection principle says that it is possible to find sets that resemble the class of all sets. There are several different forms of the reflection principle depending on exactly what is meant by "resemble". Weak forms of the reflection principle are theorems of ZF set theory due to Montague (1961), while stronger forms can be new and very powerful axioms for set theory.
The name "reflection principle" comes from the fact that properties of the universe of all sets are "reflected" down to a smaller set.
Read more about Reflection Principle: Motivation For Reflection Principles, The Reflection Principle As A Theorem of ZFC, Reflection Principles As New Axioms
Famous quotes containing the words reflection and/or principle:
“It seems certain, that though a man, in a flush of humour, after intense reflection on the many contradictions and imperfections of human reason, may entirely renounce all belief and opinion, it is impossible for him to persevere in this total scepticism, or make it appear in his conduct for a few hours.”
—David Hume (1711–1776)
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