On nonstructure of elementary submodels of a stable homogeneous structure

• Autorzy: Tapani Hyttinen
• Języki publikacji: EN

Abstrakty

EN

We assume that M is a stable homogeneous model of large cardinality. We prove a nonstructure theorem for (slightly saturated) elementary submodels of M, assuming M has dop. We do not assume that th(M) is stable.

Kategorie tematyczne

• 03C52: Properties of classes of models
• 03C45: Classification theory, stability and related concepts

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1998
• Tom: 156
• Numer: 2
• Strony: 167-182

Daty

wydano

1998

otrzymano

1997-04-01

poprawiono

1997-09-21

poprawiono

1997-10-27

Twórcy

autor

Tapani Hyttinen

• Department of Mathematics, P.O. Box 4, 00014 University of Helsinki, Finland

Bibliografia

• [Hy1] T. Hyttinen, Splitting in stable homogeneous models of unstable theories, manuscript.
• [Hy2] T. Hyttinen, On elementary submodels of a stable homogeneous structure, manuscript.
• [HS] T. Hyttinen and S. Shelah, Strong splitting in stable homogeneous models, submitted.
• [HT] T. Hyttinen and H. Tuuri, Constructing strongly equivalent nonisomorphic models for unstable theories, Ann. Pure Appl. Logic 52 (1990), 203-248.
• [NS] M. Nadel and J. Stavi, $L_∞λ$-equivalence, isomorphism and potential isomorphism, Trans. Amer. Math. Soc. 236 (1978), 51-74.
• [Sh1] S. Shelah, Finite diagrams stable in power, Ann. Math. Logic 2 (1970), 69-118.
• [Sh2] S. Shelah, Classification Theory, 2nd rev. ed., Stud. Logic Found. Math. 92, North-Holland, Amsterdam, 1990.
• [Sh3] S. Shelah, Non-structure theory, to appear.