2006/05/16 by D. W. Cunningham, Cunningham, D. W.
Mathematics · #03E15 (Primary) #03E45 #03E60 (Secondary) #FOS: Mathematics #Logic (math.LO) #math.LO #msc:03E15 #msc:03E45 #msc:03E60
paper · pdf · doi:10.48550/arxiv.math/0605445
40 pages
arxiv created 2006/05/16 · arxiv updated 2009/12/01
This article is Part I in a series of three papers devoted to determining the minimal complexity of scales in the inner model K(ℝ). Here, in Part I, we shall complete our development of a fine structure theory for K(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(ℝ): If M is an iterable real premouse, then 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(ℝ).