2006/03/29 by Arnold W. Miller, Miller, Arnold W.
Computer Science · Mathematics · #03E17 #03E50 #54D20 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Limits and Structures in Graph Theory #Logic (math.LO) #math.LO #msc:03E17 #msc:03E50 #msc:54D20
paper · pdf · doi:10.48550/arxiv.math/0603691
LaTex2e: 16 pages Latest version at http://www.math.wisc.edu/~miller
arxiv created 2006/03/29 · openalex publication_date 2006/03/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove a variety of results concerning singular sets of reals. Our results concern: Kysiak and Laver-null sets, Kocinac and gamma-k-sets, Fleissner and square Q-sets, Alikhani-Koopaei and minimal Q-like-sets, Rubin and sigma-sets, and Zapletal and the Souslin number. In particular we show that sigma-sets are Laver-null, the union of gamma-k-sets need not be gamma-k, the existence of Q-set implies an omega1-universal Gdelta, minimal Q-like sets which are not Q-sets exist, thin sets need not exist, and sn* is bounded by the cardinality of the smallest nonmeager set.