Notre Dame Journal of Formal Logic

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

Tapani Hyttinen


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

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

First available in Project Euclid: 18 December 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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.

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