Mathematics – Logic
Scientific paper
2006-04-04
Mathematics
Logic
24 pages. Final version accepted by editors for publication in Trans. AMS Random gaps homepage: http://homepage.univie.ac.at
Scientific paper
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).
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