L - like Combinatorial Principles and Level by Level Equivalence ∗ †
نویسنده
چکیده
We force and construct a model in which GCH and level by level equivalence between strong compactness and supercompactness hold, along with certain additional “L-like” combinatorial principles. In particular, this model satisfies the following properties: 1. ♦δ holds for every successor and Mahlo cardinal δ. 2. There is a stationary subset S of the least supercompact cardinal κ0 such that for every δ ∈ S, ¤δ holds and δ carries a gap 1 morass. 3. A weak version of ¤δ holds for every infinite cardinal δ. 4. There is a locally defined well-ordering of the universe W, i.e., for all κ ≥ א2 a regular cardinal, W 1 H(κ+) is definable over the structure 〈H(κ+),∈〉 by a parameter free formula. ∗2000 Mathematics Subject Classifications: 03E35, 03E55. †
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