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Characterizing an ℵ ∈ -saturated model of superstable NDOP theories by its\(\mathbb{L}_{\infty ,\aleph _ \in ^ - } \)-theory

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Abstract

Assume a complete countable first order theory is superstable with NDOP. We know that any ℵ ∈ -saturated model of the theory is ℵ ∈ -prime over a non-forking tree of “small” models and its isomorphism type can be characterized by its\(\mathbb{L}_{\infty ,k} \) (dimension qualifiers)-theory, or, if you prefer, appropriate cardinal invariants. We go one step further by providing cardinal invariants which are as finitary as seem reasonable.

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References

  1. J. T. Baldwin, M. C. Laskowski and S. Shelah,Forcing isomorphism, Journal of Symbolic Logic58 (1993), 1291–1301; math.LO/9301208.

    Article  MATH  MathSciNet  Google Scholar 

  2. S. Buechler and S. Shelah,On the existence of regular types, Annals of Pure and Applied Logic45 (1989), 277–308.

    Article  MATH  MathSciNet  Google Scholar 

  3. S. Shelah, Existence of manyL ∞,λ-equivalent, nonisomorphic models of T of power λ, Proceedings of the Model Theory Conference, Trento, June 1986, Annals of Pure and Applied Logic34 (1987), 291–310.

    Article  MATH  MathSciNet  Google Scholar 

  4. S. Shelah, On the number of strongly ℵ ∈ -saturated models of power λ, Annals of Pure and Applied Logic36 (1987), 279–287; see also [Sh:225a].

    Article  MATH  MathSciNet  Google Scholar 

  5. S. Shelah,Classification theory and the number of nonisomorphic models, Volume 92 ofStudies in Logic and the Foundations of Mathematics, North-Holland Publishing Co., Amsterdam, 1990, xxxiv+705 pp.

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Authors and Affiliations

  1. Institute of Mathematics, The Hebrew University of Jerusalem, 91904, Jerusalem, Israel

    Saharon Shelah

  2. Department of Mathematics, Rutgers University, 08854, New Brunswick, NJ, USA

    Saharon Shelah

  3. MSRI, 1000 Centennial Drive, 94720, Berkeley, CA, USA

    Saharon Shelah

Authors
  1. Saharon Shelah
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Partially supported by the United States-Israel Binational Science Foundation and the NSF. The author thanks Alice Leonhardt for the beautiful typing.

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Shelah, S. Characterizing an ℵ ∈ -saturated model of superstable NDOP theories by its\(\mathbb{L}_{\infty ,\aleph _ \in ^ - } \)-theory. Isr. J. Math. 140, 61–111 (2004). https://doi.org/10.1007/BF02786627

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  • DOI: https://doi.org/10.1007/BF02786627

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