On nonstructure of elementary submodels of a stable homogeneous structure

Tapani Hyttinen

Fundamenta Mathematicae (1998)

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

Abstract

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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.

How to cite

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Hyttinen, 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

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  1. [Hy1] T. Hyttinen, Splitting in stable homogeneous models of unstable theories, manuscript. 
  2. [Hy2] T. Hyttinen, On elementary submodels of a stable homogeneous structure, manuscript. 
  3. [HS] T. Hyttinen and S. Shelah, Strong splitting in stable homogeneous models, submitted. Zbl0961.03028
  4. [HT] T. Hyttinen and H. Tuuri, Constructing strongly equivalent nonisomorphic models for unstable theories, Ann. Pure Appl. Logic 52 (1990), 203-248. Zbl0735.03016
  5. [NS] M. Nadel and J. Stavi, L ∞ λ -equivalence, isomorphism and potential isomorphism, Trans. Amer. Math. Soc. 236 (1978), 51-74. Zbl0381.03024
  6. [Sh1] S. Shelah, Finite diagrams stable in power, Ann. Math. Logic 2 (1970), 69-118. Zbl0204.31104
  7. [Sh2] S. Shelah, Classification Theory, 2nd rev. ed., Stud. Logic Found. Math. 92, North-Holland, Amsterdam, 1990. 
  8. [Sh3] S. Shelah, Non-structure theory, to appear. 

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