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:
“The universe is the externisation of the soul. Wherever the life is, that bursts into appearance around it. Our science is sensual, and therefore superficial. The earth, and the heavenly bodies, physics, and chemistry, we sensually treat, as if they were self-existent; but these are the retinue of that Being we have.”
—Ralph Waldo Emerson (1803–1882)