In mathematics, the constructible universe (or Gödel's constructible universe), denoted L, is a particular class of sets which can be described entirely in terms of simpler sets. It was introduced by Kurt Gödel in his 1938 paper "The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis". In this, he proved that the constructible universe is an inner model of ZF set theory, and also that the axiom of choice and the generalized continuum hypothesis are true in the constructible universe. This shows that both propositions are consistent with the basic axioms of set theory, if ZF itself is consistent. Since many other theorems only hold in systems in which one or both of the propositions is true, their consistency is an important result.
Read more about Constructible Universe: What Is L?, Additional Facts About The Sets Lα, L Is A Standard Inner Model of ZFC, L Is Absolute and Minimal, L Can Be Well-ordered, L Has A Reflection Principle, Constructible Sets Are Definable From The Ordinals, Relative Constructibility
Famous quotes containing the word universe:
“For the universe has three children, born at one time, which reappear, under different names, in every system of thought, whether they be called cause, operation, and effect; or, more poetically, Jove, Pluto, Neptune; or, theologically, the Father, the Spirit, and the Son; but which we will call here, the Knower, the Doer, and the Sayer. These stand respectively for the love of truth, for the love of good, and for the love of beauty.”
—Ralph Waldo Emerson (1803–1882)