2006/04/04 by James Hirschorn, Hirschorn, James
Mathematics · #03E05 (Primary) #03E40 #28E15 #60H30 (Secondary) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Logic (math.LO) #math.CA #math.LO #msc:03E05 #msc:03E40 #msc:28E15 #msc:60H30
paper · pdf · doi:10.48550/arxiv.math/0604085
24 pages. Final version accepted by editors for publication in Trans. AMS Random gaps homepage: http://homepage.univie.ac.at/james.hirschorn/research/random.gap/random.gap.html
arxiv created 2007/10/28 · arxiv updated 2009/12/01
It is proved that there exists an (omega-1,omega-1) Souslin gap in the Boolean algebra (L(nu)/Fin,subseteq^*ae) for every nonseparable measure nu. Thus a Souslin, also known as destructible, (omega-1,omega-1) gap in P(N)/Fin can always be constructed from uncountably many random reals. We explain how to obtain the corresponding conclusion from the hypothesis that Lebesgue measure can be extended to all subsets of the real line (RVM).