arXiv 0906.35732009-06math.LO

A Topology for Galois Types in AECs

Michael Lieberman

备注：: 17 pages with references. Drawn from author's PhD thesis, "Topological and Category-Theoretic Aspects of Abstract Elementary Classes," University of Michigan, 2009. Minor edits February 2010

英文摘要：

We present a way of topologizing sets of Galois types over structures in abstract elementary classes with amalgamation. In the elementary case, the topologies thus produced refine the syntactic topologies familiar from first order logic. We exhibit a number of natural correspondences between the model-theoretic properties of classes and their constituent models and the topological properties of the associated spaces. Tameness of Galois types, in particular, emerges as a topological separation principle.

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