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The Chang-Los-Suszko Theorem in a Topological Setting
The Chang-Łoś-Suszko theorem of first-order model theory characterizes universal-existential classes of models as just those elementary classes that are closed under unions of chains. This theorem can then be used to equate two model-theoretic closure conditions for elementary classes; namely unions of chains and existential substructures. In the present paper we prove a topological analogue and indicate some applications
Categoricity and multidimensional diagrams
We study multidimensional diagrams in independent amalgamation in the
framework of abstract elementary classes (AECs). We use them to prove the
eventual categoricity conjecture for AECs, assuming a large cardinal axiom.
More precisely, we show assuming the existence of a proper class of strongly
compact cardinals that an AEC which has a single model of some high-enough
cardinality will have a single model in any high-enough cardinal. Assuming a
weak version of the generalized continuum hypothesis, we also establish the
eventual categoricity conjecture for AECs with amalgamation.Comment: 63 page
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