Statements true in L
Here is a list of propositions that hold in the constructible universe (denoted L):
- The generalized continuum hypothesis and as a consequence
- The axiom of choice
- Global square
- The existence of morasses
- The negation of the Souslin conjecture
- The non-existence of 0# and as a consequence
- The truth of Whitehead's conjecture that every abelian group A with Ext1(A, Z) = 0 is a free abelian group.
- The existence of a definable well-order of all sets (the formula for which can be given explicitly). In particular, L satisfies V=HOD.
Accepting the axiom of constructibility (which asserts that every set is constructible) these propositions also hold in the von Neumann universe, resolving many propositions in set theory and some interesting questions in analysis.