Journal of Symbolic Logic · 2001 · 35 citations · 3 references
Natural SciencesMathematicsNumber TheoryPhilosophy Of MathematicsSet TheoryAxiomatic Set TheoryCardinal NumbersLarge CardinalsModel TheoryOrdinal NumbersConsistencyConsistency Strength Of Large CardinalsProper ForcingWoodin Cardinals
Abstract We present two ways in which the model L (ℝ) is canonical assuming the existence of large cardinals. We show that the theory of this model, with ordinal parameters, cannot be changed by small forcing: we show further that a set of ordinals in V cannot be added to L (ℝ) by small forcing. The large cardinal needed corresponds to the consistency strength of AD L (ℝ) : roughly ω Woodin cardinals.
3
Donald A. Martin, John R. Steel · Journal of the American Mathematical Society · 1994 · 85 citations
Inner models with many Woodin cardinals
John R. Steel · Annals of Pure and Applied Logic · 1993 · 82 citations