Scales and the fine structure of K(R). Part II: Weak real mice and scales

2006/05/16 by D. W. Cunningham, Daniel W. Cunningham, Cunningham, D. W.
Mathematics · #03E15 (Primary) #03E45 #03E60 (Secondary) #Advanced Topology and Set Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #advanced mathematical theories #math.LO #msc:03E15 #msc:03E45 #msc:03E60

paper · pdf · doi:10.48550/arxiv.math/0605448

27 pages

arxiv created 2006/05/16 · openalex publication_date 2006/05/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define weak real mice M and prove that the boldface pointclass \boldsymbolΣ_m(M) has the scale property assuming only the determinacy of sets of reals in M when m is the smallest integer m>0 such that \boldsymbolΣ_m(M) contains a set of reals not in M. We shall use this development in Part III to obtain scales of minimal complexity in K(ℝ).

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