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CONSTRUCTING MANY ATOMIC MODELS IN ℵ1

Published online by Cambridge University Press:  14 September 2016

JOHN T. BALDWIN
Affiliation:
DEPARTMENT OF MATHEMATICS, STATISTICS, AND COMPUTER SCIENCE UNIVERSITY OF ILLINOIS AT CHICAGO 851 S. MORGAN CHICAGO, IL 60607, USA E-mail: jbaldwin@uic.edu URL: http://homepages.math.uic.edu/∼jbaldwin/
MICHAEL C. LASKOWSKI
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF MARYLAND COLLEGE PARK, MD 20742-4015, USA E-mail: mcl@math.umd.edu URL: http://www.math.umd.edu/∼laskow/
SAHARON SHELAH
Affiliation:
HEBREW UNIVERSITY (AND RUTGERS UNIVERSITY) EINSTEIN INSTITUTE OF MATHEMATICS GIVAT RAM, JERUSALEM, 9190401, ISRAEL E-mail: shelah@math.huji.ac.il URL: http://shelah.logic.at/

Abstract

We introduce the notion of pseudoalgebraicity to study atomic models of first order theories (equivalently models of a complete sentence of ${L_{{\omega _1},\omega }}$ ). Theorem: Let T be any complete first-order theory in a countable language with an atomic model. If the pseudominimal types are not dense, then there are 20 pairwise nonisomorphic atomic models of T, each of size ℵ1.

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Articles
Copyright
Copyright © The Association for Symbolic Logic 2016 

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