# Category: Constructible universe

Diamond principle
In mathematics, and particularly in axiomatic set theory, the diamond principle ◊ is a combinatorial principle introduced by Ronald Jensen in that holds in the constructible universe (L) and that impl
Axiom of constructibility
The axiom of constructibility is a possible axiom for set theory in mathematics that asserts that every set is constructible. The axiom is usually written as V = L, where V and L denote the von Neuman
Square principle
In mathematical set theory, a square principle is a combinatorial principle asserting the existence of a cohering sequence of short closed unbounded (club) sets so that no one (long) club set coheres
Condensation lemma
In set theory, a branch of mathematics, the condensation lemma is a result about sets in theconstructible universe. It states that if X is a transitive set and is an elementary submodel of some level
Constructible universe
In mathematics, in set theory, the constructible universe (or Gödel's constructible universe), denoted by L, is a particular class of sets that can be described entirely in terms of simpler sets. L is
Gödel operation
In mathematical set theory, a set of Gödel operations is a finite collection of operations on sets that can be used to construct the constructible sets from ordinals. Gödel introduced the original set
Minimal model (set theory)
In set theory, a branch of mathematics, the minimal model is the minimal standard model of ZFC.The minimal model was introduced by Shepherdson and rediscovered by . The existence of a minimal model ca
Zero sharp
In the mathematical discipline of set theory, 0# (zero sharp, also 0#) is the set of true formulae about indiscernibles and order-indiscernibles in the Gödel constructible universe. It is often encode
Silver machine
In set theory, Silver machines are devices used for bypassing the use of fine structure in proofs of statements holding in L. They were invented by set theorist Jack Silver as a means of proving globa
Jensen hierarchy
In set theory, a mathematical discipline, the Jensen hierarchy or J-hierarchy is a modification of Gödel's constructible hierarchy, L, that circumvents certain technical difficulties that exist in the