266,833 research outputs found
A presentation theorem for continuous logic and Metric Abstract Elementary Classes
We give a presentation theorem for continuous first-order logic and Metric
Abstract Elementary classes in terms of and Abstract
Elementary Classes, respectively. This presentation is accomplished by
analyzing dense subsets that are closed under functions. We extend this
correspondence to types and saturation
Tameness and frames revisited
We study the problem of extending an abstract independence notion for types
of singletons (what Shelah calls a good frame) to longer types. Working in the
framework of tame abstract elementary classes, we show that good frames can
always be extended to types of independent sequences. As an application, we
show that tameness and a good frame imply Shelah's notion of dimension is
well-behaved, complementing previous work of Jarden and Sitton. We also improve
a result of the first author on extending a frame to larger models.Comment: 36 page
Structural Logic and Abstract Elementary Classes with Intersection
We give a syntactic characterization of abstract elementary classes (AECs)
closed under intersections using a new logic with a quantifier for isomorphism
types that we call structural logic: we prove that AECs with intersections
correspond to classes of models of a universal theory in structural logic. This
generalizes Tarski's syntactic characterization of universal classes. As a
corollary, we obtain that any AEC with countable L\"owenheim-Skolem number is
axiomatizable in , where is the quantifier
"there exists uncountably many".Comment: 14 page
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