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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the prime model property


Author: Ludomir Newelski
Journal: Proc. Amer. Math. Soc. 124 (1996), 2519-2525
MSC (1991): Primary 03C15, 03C45
MathSciNet review: 1322936
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Abstract: Assume $T$ is superstable, $\Phi (x)$ is a formula over $\emptyset $, $Q=\Phi (M^*)$ is countable and $K_Q=\{M: M$ is countable and $\Phi (M)=Q\}$. We investigate models in $K_Q$ assuming $K_Q$ has the prime model property. We prove some corollaries on the number of models in $K_Q$. We show an example of an $\omega $-stable $T$ and $Q$ with $K_Q$ having exactly 3 models.


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Additional Information

Ludomir Newelski
Affiliation: Mathematical Institute, Polish Academy of Sciences, ul.Kopernika 18, 51-617 Wroclaw, Poland
Address at time of publication: Mathematical Institute, Wrocław University, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Email: newelski@math.uni.wroc.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03311-4
PII: S 0002-9939(96)03311-4
Received by editor(s): August 26, 1994
Received by editor(s) in revised form: February 13, 1995
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1996 American Mathematical Society