## 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

https://projecteuclid.org/euclid.ndjfl/1040248458

Digital Object Identifier
doi:10.1305/ndjfl/1040248458

Mathematical Reviews number (MathSciNet)
MR1345748

Zentralblatt MATH identifier
0854.03031

#### 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. https://projecteuclid.org/euclid.ndjfl/1040248458

#### References

• Baldwin, J., Fundamentals of Stability Theory, Springer-Verlag, London, 1988. Zbl 0685.03024 MR 89k:03002
• Bouscaren, E., and E. Hrushovski, “On one-based theories,” The Journal of Symbolic Logic vol. 59 (1994), pp. 579–595. Zbl 0832.03017 MR 95e:03103
• Hart, B., A. Pillay and S. Starchenko, “1-based theories: The Main Gap for a-models,” forthcoming in Archives for Mathematical Logic. Zbl 0849.03022 MR 96i:03030
• Shelah, S., Classification Theory, Studies in the Logical Foundations of Mathematics 92, second revised edition, North-Holland, Amsterdam, 1990. Zbl 0388.03009 MR 91k:03085