# On nonstructure of elementary submodels of a stable homogeneous structure

Fundamenta Mathematicae (1998)

- Volume: 156, Issue: 2, page 167-182
- ISSN: 0016-2736

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topHyttinen, Tapani. "On nonstructure of elementary submodels of a stable homogeneous structure." Fundamenta Mathematicae 156.2 (1998): 167-182. <http://eudml.org/doc/212266>.

@article{Hyttinen1998,

abstract = {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.},

author = {Hyttinen, Tapani},

journal = {Fundamenta Mathematicae},

keywords = {stable homogeneous model; DOP; nonstructure theorem; dimensional order property},

language = {eng},

number = {2},

pages = {167-182},

title = {On nonstructure of elementary submodels of a stable homogeneous structure},

url = {http://eudml.org/doc/212266},

volume = {156},

year = {1998},

}

TY - JOUR

AU - Hyttinen, Tapani

TI - On nonstructure of elementary submodels of a stable homogeneous structure

JO - Fundamenta Mathematicae

PY - 1998

VL - 156

IS - 2

SP - 167

EP - 182

AB - 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.

LA - eng

KW - stable homogeneous model; DOP; nonstructure theorem; dimensional order property

UR - http://eudml.org/doc/212266

ER -

## References

top- [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. Zbl0961.03028
- [HT] T. Hyttinen and H. Tuuri, Constructing strongly equivalent nonisomorphic models for unstable theories, Ann. Pure Appl. Logic 52 (1990), 203-248. Zbl0735.03016
- [NS] M. Nadel and J. Stavi, ${L}_{\infty}\lambda $-equivalence, isomorphism and potential isomorphism, Trans. Amer. Math. Soc. 236 (1978), 51-74. Zbl0381.03024
- [Sh1] S. Shelah, Finite diagrams stable in power, Ann. Math. Logic 2 (1970), 69-118. Zbl0204.31104
- [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.

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