Constructible universe

In mathematics, the constructible universe (or Gödel's constructible universe) is a particular class of sets which can be described entirely in terms of simpler sets. It was introduced by Kurt Gödel in his 1940 paper Consistency of the axiom of choice and of the generalized continuum-hypothesis with the axioms of set theory. In this, he proved that the constructible universe is a model of 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. Since many other theorems only hold in systems in which one or both of the propositions is true, their consistency is an important result.

Let x represent the set of all finite non-reproducible sets. Let S(x;n) represent the set of finite non-reproducible sets taken over the field of real numbers. Then S(n;n) is not admittive of all possible universes of sets that do not include S(n;n) as a possible finite reproducible subset. Mamoun's Eternal Party Method innovation to Goedel's theorem was to point out that S(n; not n), taken over the field of real numbers leads to a non-ergodic finite state of dimensional indeterminacy that co-incides in all cases except S(n;n), interpreted as to content in terms of determinate finite states, with the resultant universe of reproducible sets. This likewise corresponds with the Monster Set but, remarkably, compactifies the set to include a self-referential mapping of the set configuration states such that the Monster Set - S(n;n) complements are mappings that are mutually onto and into; this is equivalent to a finite state indeterminacy in all forms except the union of determinate and indeterminate states, which maintains supersymmetric conservation parity of all dynamic states taken over the field of complex numbers. The immediate application to D-brane anti-deSitter spaces allows for a non-ergodic complete state manifold capable of describing any cyclically descriptive dynamic (1...n-1) when taken over the field of Monster Set classes of determinate states.