On the prime model property
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- by Ludomir Newelski PDF
- Proc. Amer. Math. Soc. 124 (1996), 2519-2525 Request permission
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.References
- John T. Baldwin, Fundamentals of stability theory, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1988. MR 918762, DOI 10.1007/978-3-662-07330-8
- Wilfrid Hodges, I. M. Hodkinson, and Dugald Macpherson, Omega-categoricity, relative categoricity and coordinatisation, Ann. Pure Appl. Logic 46 (1990), no. 2, 169–199. MR 1042608, DOI 10.1016/0168-0072(90)90033-X
- Ludomir Newelski, A model and its subset, J. Symbolic Logic 57 (1992), no. 2, 644–658. MR 1169199, DOI 10.2307/2275297
- Ludomir Newelski, Scott analysis of pseudotypes, J. Symbolic Logic 58 (1993), no. 2, 648–663. MR 1233930, DOI 10.2307/2275225
- Ludomir Newelski, Meager forking, Ann. Pure Appl. Logic 70 (1994), no. 2, 141–175. MR 1321462, DOI 10.1016/0168-0072(94)90028-0
- L. Newelski, On atomic or saturated sets, J. Symb. Logic, submitted.
- Gerald E. Sacks, Saturated model theory, Mathematics Lecture Note Series, W. A. Benjamin, Inc., Reading, Mass., 1972. MR 0398817
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
- Received by editor(s): August 26, 1994
- Received by editor(s) in revised form: February 13, 1995
- Communicated by: Andreas R. Blass
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 2519-2525
- MSC (1991): Primary 03C15, 03C45
- DOI: https://doi.org/10.1090/S0002-9939-96-03311-4
- MathSciNet review: 1322936