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DISJOINT AMALGAMATION IN LOCALLY FINITE AEC

Published online by Cambridge University Press:  21 March 2017

JOHN T. BALDWIN ,
MARTIN KOERWIEN  and
MICHAEL C. LASKOWSKI
JOHN T. BALDWIN
Affiliation:
DEPARTMENT OF MATHEMATICS, STATISTICS AND COMPUTER SCIENCE M/C 249 UNIVERSITY OF ILLINOIS AT CHICAGO 851 S. MORGAN STREET CHICAGO, IL 60607, USA E-mail: jbaldwin@uic.edu
MARTIN KOERWIEN
Affiliation:
UNIVERSITÄT WIENKURT GÖDEL RESEARCH CENTER FOR MATHEMATICAL LOGIC WÄHRINGER STRASSE 25, 1090 WIEN, AUSTRIA E-mail: kwienmart@gmail.com
MICHAEL C. LASKOWSKI
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF MARYLAND COLLEGE PARK, MD 20742, USA E-mail: mcl@math.umd.edu
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Abstract

We introduce the concept of a locally finite abstract elementary class and develop the theory of disjoint $\left( { \le \lambda ,k} \right)$ -amalgamation) for such classes. From this we find a family of complete ${L_{{\omega _1},\omega }}$ sentences ${\phi _r}$ that a) homogeneously characterizes ${\aleph _r}$ (improving results of Hjorth [11] and Laskowski–Shelah [13] and answering a question of [21]), while b) the ${\phi _r}$ provide the first examples of a class of models of a complete sentence in ${L_{{\omega _1},\omega }}$ where the spectrum of cardinals in which amalgamation holds is other that none or all.

Keywords

03C4803C75characterize cardinalsamalgamationabstract elementary classesL ω1ω

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Type
Articles
Information
The Journal of Symbolic Logic , Volume 82 , Issue 1 , March 2017 , pp. 98 - 119
Copyright
Copyright © The Association for Symbolic Logic 2017 

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References

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