Gianluca Paolini

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Systems In this chapter we define the abstract versions of the systems that we are going to deal with for the rest of the thesis. They qualify as abstract because their semantics intend to give an abstract account of the concepts of dependence and independence, and do not refer to any particular version of these notions. The variants of dependence and(More)
We prove that if G is a Polish group and A a group admitting a system of generators whose associated length function satisfies: (i) if 0 < k < ω, then lg(x) ≤ lg(xk); (ii) if lg(y) < k < ω and xk = y, then x = e, then there exists a subgroup G∗ of G of size b (the bounding number) such that G∗ is not embeddable in A. In particular, we prove that the(More)
We present a framework for studying the concept of independence in a general context covering database theory, algebra and model theory as special cases. We show that well-known axioms and rules of independence for making inferences concerning basic atomic independence statements are complete with respect to a variety of semantics. Our results show that the(More)
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