On absolutely $Δ^1_2$ operations

On Absolutely Continuous Transformations

On absolutely universal embeddings

It is well known that, given a point-line geometry Γ and a projective embedding ε : Γ → PG(V ), if dim(V ) equals the size of a generating set of Γ, then ε is not derived from any other embedding. Thus, if Γ admits an absolutely universal embedding, then ε is absolutely universal. In this paper, without assuming the existence of any absolutely universal embedding, we give sufficient conditions ...

On Absolutely Divergent Series

We show that in the א2-stage countable support iteration of Mathias forcing over a model of CH the complete Boolean algebra generated by absolutely divergent series under eventual dominance is not isomorphic to the completion of P (ω)/fin. This complements Vojtáš’ result, that under cf(c) = p the two algebras are isomorphic [15].

On Absolutely Convergent Dirichlet Series

satisfying zZ\ \^A < °°, if and only if f is) is bounded away from zero in the half-plane 0-3:0. This discovery amounts to a determination of the spectrum of the Banach-algebra element associated with fis), and it thus makes available for the theory of ordinary Dirichlet series the well-known theorem of Gelfand on analytic functions of Banach-algebra elements (see §24D of [7]) and its generaliz...

Absolutely Rigid Systems and Absolutely Indecomposable Groups

We give a new proof that there are arbitrarily large indecomposable abelian groups; moreover, the groups constructed are absolutely indecomposable, that is, they remain indecomposable in any generic extension. However, any absolutely rigid family of groups has cardinality less than the partition cardinal κ(ω). Added December 2004: The proofs of Theorems 0.2 and 0.3 are not correct, and the clai...