L(R)

Construction

Assumptions

Results

• Every projective set of reals -- and therefore every analytic set and every Borel set of reals -- is an element of L.
• Every set of reals in L is Lebesgue measurable and has the property of Baire and the perfect set property.
• L does not satisfy the axiom of uniformization or the axiom of real determinacy.
• R^#, the sharp of the set of all reals, has the smallest Wadge degree of any set of reals not contained in L.
• While not every relation on the reals in L has a uniformization in L, every such relation does have a uniformization in L.
• Given any generic extension V of V, L is an elementary submodel of L as calculated in V. Thus the theory of L cannot be changed by forcing.
• L satisfies AD+.