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A topology for galois types in abstract elementary classes
Author(s) -
Lieberman Michael
Publication year - 2011
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200910132
Subject(s) - mathematics , topology (electrical circuits) , network topology , order (exchange) , galois module , pure mathematics , fundamental theorem of galois theory , galois group , embedding problem , combinatorics , computer science , operating system , finance , economics
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. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim