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:
“But before the extremity of the Cape had completely sunk, it appeared like a filmy sliver of land lying flat on the ocean, and later still a mere reflection of a sand-bar on the haze above. Its name suggests a homely truth, but it would be more poetic if it described the impression which it makes on the beholder.”
—Henry David Thoreau (1817–1862)
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—Ezra Pound (1885–1972)