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:
“In his comprehensive delight in all experience Dickens resembles Walt Whitman, but he was innocent of that nebulous transcendentalism that blurred Whitman’s universe into vast misty panoramas and left him, for all his huge democratic vistas, unable to tell a story or paint a single concrete human being.”
—Edgar Johnson (1912–1990)