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Asymmetric RK-minimal types

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Abstract

We consider semi-isolation on the locus of a strongly non-isolated, RK-minimal type in a small theory, and we prove that its asymmetry (as a binary relation) is caused by a specific form of the strict order property: the partial definability of semi-isolation.

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References

  1. Benda M.: Remarks on countable models. Fund. Math. 81, 107–119 (1974)

    MATH  MathSciNet  Google Scholar 

  2. Pillay A.: Theories with exactly three countable models and theories with algebraic prime models. J. Symbolic Log. 45, 302–310 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  3. Pillay A.: Countable models of stable theories. Proc. Am. Math. Soc. 89, 666–672 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  4. Pillay, A.: Countable models of 1-based theories, preprint (1988)

  5. Sudoplatov S.: On powerful types in small theories (in Russian). Siberian Math. J. 31, 118–128 (1990)

    MathSciNet  Google Scholar 

  6. Sudoplatov, S.: The Lachlan Problem, 245p. Novosibirsk (2008)

  7. Tanović P.: On constants and the strict order property. Arch. Math. Log. 45, 423–430 (2006)

    Article  MATH  Google Scholar 

  8. Tanović P.: Theories with constants and three countable models. Arch. Math. Log. 46, 517–527 (2007)

    Article  MATH  Google Scholar 

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Correspondence to Predrag Tanović.

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The author was supported by the Ministry of Science and Technology of Serbia, project 144013.

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Tanović, P. Asymmetric RK-minimal types. Arch. Math. Logic 49, 367–377 (2010). https://doi.org/10.1007/s00153-010-0176-9

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  • DOI: https://doi.org/10.1007/s00153-010-0176-9

Keywords

Mathematics Subject Classification (2000)