Scales and the fine structure of K(R). Part I: Acceptability above the reals

Details Scales and the fine structure of K(R). Part I: Acceptability above the reals Scales and the fine structure of K(R). Part I: Acceptability above the reals

2006-05-16

arxiv.org/abs/math/0605445v1

Mathematics

Logic

40 pages

Scientific paper

This article is Part I in a series of three papers devoted to determining the minimal complexity of scales in the inner model $K(\mathbb{R})$. Here, in Part I, we shall complete our development of a fine structure theory for $K(\mathbb{R})$ which is essential for our work in Parts II and III. In particular, we prove the following fundamental theorem which supports our analysis of scales in $K(\mathbb{R})$: If $\mathcal{M}$ is an iterable real premouse, then $\mathcal{M}$ is acceptable above the reals. This theorem will be used in Parts II and III to solve the problem of finding scales of minimal complexity in $K(\mathbb{R})$.

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