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CONSTRUCTING MANY ATOMIC MODELS IN ℵ1

Published online by Cambridge University Press:  14 September 2016

JOHN T. BALDWIN ,
MICHAEL C. LASKOWSKI  and
SAHARON SHELAH
JOHN T. BALDWIN
Affiliation:
DEPARTMENT OF MATHEMATICS, STATISTICS, AND COMPUTER SCIENCE UNIVERSITY OF ILLINOIS AT CHICAGO 851 S. MORGAN CHICAGO, IL60607, USAE-mail: jbaldwin@uic.eduURL: http://homepages.math.uic.edu/∼jbaldwin/
MICHAEL C. LASKOWSKI
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF MARYLAND COLLEGE PARK, MD20742-4015, USAE-mail: mcl@math.umd.eduURL: http://www.math.umd.edu/∼laskow/
SAHARON SHELAH
Affiliation:
HEBREW UNIVERSITY (AND RUTGERS UNIVERSITY) EINSTEIN INSTITUTE OF MATHEMATICS GIVAT RAM, JERUSALEM, 9190401, ISRAELE-mail: shelah@math.huji.ac.ilURL: http://shelah.logic.at/
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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 2ℵ0 pairwise nonisomorphic atomic models of T, each of size ℵ1.

Keywords

infinitary logicatomic modelspseudo-minimalityforcing
Type
Articles
Information
The Journal of Symbolic Logic , Volume 81 , Issue 3 , September 2016 , pp. 1142 - 1162
Copyright
Copyright © The Association for Symbolic Logic 2016 

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