Notre Dame Journal of Formal Logic

Remarks on Structure Theorems for $\omega_{1}$-Saturated Models

Tapani Hyttinen

Abstract

We give a characterization for those stable theories whose $\omega_{1}$-saturated models have a "Shelah-style" structure theorem. We use this characterization to prove that if a theory is countable, stable, and 1-based without dop or didip, then its $\omega_{1}$-saturated models have a structure theorem. Prior to us, this is proved in a paper of Hart, Pillay, and Starchenko (in which they also count the number of models, which we do not do here). Some other remarks are also included.

Article information

Source
Notre Dame J. Formal Logic Volume 36, Number 2 (1995), 269-278.

Dates
First available in Project Euclid: 18 December 2002

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1040248458

Digital Object Identifier
doi:10.1305/ndjfl/1040248458

Mathematical Reviews number (MathSciNet)
MR1345748

Zentralblatt MATH identifier
0854.03031

Subjects
Primary: 03C50: Models with special properties (saturated, rigid, etc.)
Secondary: 03C45: Classification theory, stability and related concepts [See also 03C48] 03C52: Properties of classes of models

Citation

Hyttinen, Tapani. Remarks on Structure Theorems for $\omega_{1}$ -Saturated Models. Notre Dame J. Formal Logic 36 (1995), no. 2, 269--278. doi:10.1305/ndjfl/1040248458. http://projecteuclid.org/euclid.ndjfl/1040248458.


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References

  • [1] Baldwin, J., Fundamentals of Stability Theory, Springer-Verlag, London, 1988.
  • [2] Bouscaren, E., and E. Hrushovski, ``On one-based theories,'' The Journal of Symbolic Logic vol. 59 (1994), pp. 579--595.
  • [3] Hart, B., A. Pillay and S. Starchenko, ``1-based theories: The Main Gap for a-models,'' forthcoming in Archives for Mathematical Logic.
  • [4] Shelah, S., Classification Theory, Studies in the Logical Foundations of Mathematics 92, second revised edition, North-Holland, Amsterdam, 1990.