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On Jonsson stability and some of its generalizations

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We consider Jonsson analogues of the concepts of stability and P-stability. We also consider properties and connections of a Jonsson theory and its center that concern these concepts.

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References

  1. J. T. Baldwin, Fundamentals of Stability Theory, Springer, New York (1987).

    Google Scholar 

  2. J. Barwise, ed., Handbook of Mathematical Logic [Russian translation], Vol. 1, Model Theory, Nauka, Moscow (1982).

    Google Scholar 

  3. E. Bouscaren, “Dimensional order property and pairs of models,” Ann. Pure Appl. Logic, 41, 205–231 (1989).

    Article  MATH  MathSciNet  Google Scholar 

  4. E. Bouscaren, “Elementary pairs of models,” Ann. Pure Appl. Logic, 45, 129–137 (1989).

    Article  MATH  MathSciNet  Google Scholar 

  5. P. Eklof and G. Sabbagh, “Model completions and modules,” Ann. Math. Logic, 2, 251–295 (1971).

    Article  MATH  MathSciNet  Google Scholar 

  6. W. Hodges, Model Theory, Cambridge Univ. Press, Cambridge (1993).

    Book  MATH  Google Scholar 

  7. E. Hrushovski, Simplicity and the Lascar Group, preprint (1998).

  8. B. Jonsson, “Homogeneous universal relational systems,” Math. Scand., 8, 137–142 (1960).

    MATH  MathSciNet  Google Scholar 

  9. H. J. Keisler and C. C. Chang, Model Theory [Russian translation], Nauka, Moscow (1977).

    Google Scholar 

  10. B. Kim, “Forking in simple unstable theories,” J. London Math. Soc. (2), 57, 257–267 (1998).

    Article  MathSciNet  Google Scholar 

  11. D. W. Kueker, “Core structures for theories,” Fund. Math., 89, 154–171 (1975).

    MathSciNet  Google Scholar 

  12. A. Macintyre, “On algebraically closed groups,” Ann. Math., 96, 53–97 (1972).

    Article  MathSciNet  Google Scholar 

  13. M. Morley and R. L. Vaught, “Homogeneous universal models,” Math. Scand., 11, 37–57 (1962).

    MATH  MathSciNet  Google Scholar 

  14. T. G. Mustafin, The Stable Theories [in Russian], Karaganda (1981).

  15. T. G. Mustafin, The Number of Models of Theories [in Russian], Karaganda (1983).

  16. T. G. Mustafin, “New concepts of stability for theories,” in: Proc. Soviet-French Colloq. on Model Theory, KarGU, Karaganda (1990), pp. 112–125.

  17. T. G. Mustafin, “Generalized Jonsson conditions and the description of generalized Jonsson theories of Boolean algebras,” Mat. Tr., 1, No. 2, 135–197 (1998).

    MATH  MathSciNet  Google Scholar 

  18. Y. Mustafin, “Quelques propriétés des théories de Jonsson,” J. Symb. Logic, 67, No. 2, 528–536 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  19. T. G. Mustafin and T. A. Nurmagambetov, “On P-stability of complete theories,” in: Structure Properties of Algebraic Systems [in Russian], KarGU, Karaganda (1990), pp. 88–100.

    Google Scholar 

  20. T. A. Nurmagambetov and B. Poizat, “The number of elementary pairs over sets,” in: Research in Algebraic System Theory [in Russian], Izd. KarGU, Karaganda (1995), pp. 73–82.

    Google Scholar 

  21. A. T. Nurtazin, “On elementary pairs in uncountably categorical theories,” in: Proc. Soviet-French Colloq. on Model Theory, KarGU, Karaganda (1990), pp. 126–146.

    Google Scholar 

  22. E. A. Palyutin, “Models with countable-categorical universal theories,” Algebra Logika, 10, No. 1, 23–32 (1971).

    MATH  MathSciNet  Google Scholar 

  23. E. A. Palyutin, “E*-stable theories,” Algebra Logika, 42, No. 2, 194–210 (2003).

    MATH  MathSciNet  Google Scholar 

  24. A. Pillay, “Forking in the category of existentially closed structures,” in: A. Macintyre, ed., Connection between Model Theory and Algebraic and Analytic Geometry, Quaderni di Matematica, Vol. 6, Univ. of Naples (2000).

  25. B. Poizat, “Paires de structures stables,” J. Symb. Logic, 48, 239–249 (1983).

    Article  MATH  MathSciNet  Google Scholar 

  26. D. Saracino, “Model companion for ω-categorical theories,” Proc. Am. Math. Soc., 39, 591–598 (1973).

    Article  MATH  MathSciNet  Google Scholar 

  27. S. Shelah, “The lazy model-theoretician’s guide to stability,” Log. Anal., 71-72, 241–308 (1967).

    Google Scholar 

  28. A. R. Yeshkeyev, “The perfect Jonsson theory,” in: 3th Int. Conf. on Algebra. Abstracts, Krasnoyarsk (1993).

  29. A. R. Yeshkeyev and T. G. Mustafin, “A description of Jonsson universals of unars,” in: Research in Algebraic System Theory [in Russian], Izd. KarGU, Karaganda (1995), pp. 51–57.

    Google Scholar 

  30. A. R. Yeshkeyev and T. G. Mustafin, “Some properties of Jonsson primitives of unars.” in: Research in Algebraic System Theory [in Russian], Izd. KarGU, Karaganda (1995), pp. 58–61.

    Google Scholar 

  31. A. R. Yeshkeyev and R. M. Ospanov, “Jonsson theories and their companions,” in: Proc. of 10th All-Univ. Conf. on Mathematics and Mechanics [in Russian], Vol. 1, Almaty (2005), pp. 185–190.

  32. A. R. Yeshkeyev and R. M. Ospanov, “A connection of Jonsson theories with Lindström’s theorem,” in: Proc. 5th Kazakh-French Colloq. on Model Theory, Izd. KarGU, Karaganda (2001), pp. 65–75.

  33. B. I. Zilber, “On a solution of the problem of finite axiomatizability for theories categorical in all infinite powers,” in: B. Baizanov, ed., Theory of Models and Its Application [in Russian], KazGU (1980), pp. 47–60.

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Correspondence to A. R. Yeshkeyev.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 14, No. 8, pp. 117–128, 2008.

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Yeshkeyev, A.R. On Jonsson stability and some of its generalizations. J Math Sci 166, 646–654 (2010). https://doi.org/10.1007/s10958-010-9879-z

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