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We examine the splitting number (B) and the reaping number (B) of quotient Boolean algebras B = (ω)/ℐ where ℐ is an ideal or an analytic P-ideal. For instance we prove that under Martin’s Axiom ((ω)/ℐ) = for all ideals ℐ and for all analytic P-ideals ℐ with the BW property (and one cannot drop the BW assumption). On the other hand under Martin’s Axiom ((ω)/ℐ) = for all ideals and all analytic P-ideals ℐ (in this case we do not need the BW property). We also provide applications of these characteristics...
In this paper the fundamental algebraic propeties of convergent and divergent permutations of ℕ are presented. A permutation p of ℕ is said to be divergent if at least one conditionally convergent series of real terms is rearranged by p to a divergent series . All other permutations of ℕ are called convergent. Some generalizations of the Riemann theorem about the set of limit points of the partial sums of rearrangements of a given conditionally convergent series are also studied.
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