Remarks on structure theorems for \(\omega_ 1\)-saturated models. (English) Zbl 0854.03031

Hyttinen, Tapani

Notre Dame J. Formal Logic 36, No. 2, 269-278 (1995).

The paper is concerned with the problem of classifying those complete countable stable theories \(T\) whose \(\omega_1\)-saturated models satisfy a structure property SP in the sense of Shelah. Several characterizations of SP are proved when \(T\) admits both ndop and ndidip (if ndop – or ndidip – fails, then SP does not hold). This provides a new proof of a result of Hart, Pillay and Starchenko saying that, if \(T\) is 1-based (with ndop and ndidip), then the \(\omega_1\)-saturated models of \(T\) satisfy SP.

Reviewer: C.Toffalori (Camerino)

MSC:

03C45	Classification theory, stability, and related concepts in model theory
03C52	Properties of classes of models

Keywords:

\(\omega_ 1\)-saturated models; countable stable theories; structure property; ndop; ndidip

References:

[1]	Baldwin, J., Fundamentals of Stability Theory , Springer-Verlag, London, 1988. · Zbl 0685.03024
[2]	Bouscaren, E., and E. Hrushovski, “On one-based theories,” The Journal of Symbolic Logic vol. 59 (1994), pp. 579–595. JSTOR: · Zbl 0832.03017 · doi:10.2307/2275409
[3]	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 · doi:10.1007/s001530050025
[4]	Shelah, S., Classification Theory , Studies in the Logical Foundations of Mathematics 92, second revised edition, North-Holland, Amsterdam, 1990. · Zbl 0388.03009