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On the existence of atomic models

  • M. C. Laskowski (a1) and S. Shelah (a2) (a3)

Abstract

We give an example of a countable theory T such that for every cardinal λ ≥ ℵ2 there is a fully indiscernible set A of power λ such that the principal types are dense over A, yet there is no atomic model of T over A. In particular, T(A) is a theory of size λ where the principal types are dense, yet T(A) has no atomic model.

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References

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[1]Erdös, P., Hajnal, A., Mate, A., and Rado, P., Combinatorial set theory, North-Holland, Amsterdam, 1984.
[2]Knight, J., Prime and atomic models, this Journal, vol. 43 (1978), pp. 385393.
[3]Kueker, D. W., Uniform theorems in infinitary logic, Logic Colloquium '77 (Macintyre, A., Pacholski, L., and Paris, J., editors), North-Holland, Amsterdam, 1978.
[4]Kueker, D. W. and Laskowski, M. C., On generic structures, Notre Dame Journal of Formal Logic, vol. 33 (1992), pp. 175183.
[5]Shelah, S., Classification theory, North-Holland, Amsterdam, 1978.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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