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Isotyped Algebras

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References

  1. W. Hodges, Model Theory, EncyclopediaMath. Appl. (Cambridge Univ. Press, Cambridge, 1993), Vol. 42.

    Book  MATH  Google Scholar 

  2. D. Marker, Model Theory: An Introduction, Grad. Texts in Math. (Springer, New York, 2002), Vol. 217.

    MATH  Google Scholar 

  3. B. Plotkin and G. Zhitomirski, “Some Logical Invariants of Algebras and Logical Relations between Algebras,” St. Petersburg Math. J. 19(5), 829–852 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  4. B. Plotkin, Seven Lectures on the Universal Algebraic Geometry, arxiv: math.GM/0204245.

  5. B. Plotkin, “Algebraic Geometry in First Order Logic,” J. Math. Sci. (N. Y.) 137(5), 5049–5097 (2006); arxiv: math.GM/0312485.

    Article  MathSciNet  MATH  Google Scholar 

  6. B. Plotkin, “Some Results and Problems Related to Universal Algebraic Geometry,” Intern. J. Algebra Comput. 17(5–6), 1133–1164 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  7. G. Baumslag, A. Myasnikov, and V. Remeslennikov, “Algebraic Geometry Over Groups, I: Algebraic Sets and Ideal Theory,” J. Algebra 219(1), 16–79 (1999).

    Article  MathSciNet  MATH  Google Scholar 

  8. A. Kvaschuk, A. Myasnikov, and V. Remeslennikov, “Algebraic Geometry Over Groups, III: Elements of Model Theory,” J. Algebra 288(1), 78–98 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  9. A. Myasnikov and V. Remeslennikov, “Algebraic Geometry Over Groups, II: Logical Foundations,” J. Algebra 234 (1), 225–276 (2000).

    Google Scholar 

  10. B. Plotkin, Algebraic Logic, Varieties of Algebras and Algebraic Varieties, arxiv: math.GM/0312420.

  11. P. R. Halmos, Algebraic Logic (Chelsea, New York, 1962).

    MATH  Google Scholar 

  12. B. I. Plotkin, “Some Notions of Algebraic Geometry in Universal Algebra,” St. Petersburg Math. J. 9(4), 859–879 (1998).

    MathSciNet  Google Scholar 

  13. R. Grossberg, “Classification Theory for Abstract Elementary Classes,” in Logic and Algebra, Contemp. Math. 302, 165–204 (Amer. Math. Soc., Providence, R.I., 2002).

    Google Scholar 

  14. R. Baer, “Engelsche Elemente Noetherscher Gruppen,” Math. Ann. 133(3), 256–270 (1957).

    Article  MathSciNet  MATH  Google Scholar 

  15. B. I. Plotkin, “Radical and Nil-Elements in Groups,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 1, 130–135 (1958).

  16. B. I. Plotkin, “Notes on Engel Groups and Engel Elements in Groups. Some Generalizations,” Izv. Ural. Univ. Ser. Mat. Mekh. 36, 153–166 (2005); arxiv: math.GR/0406100.

    MathSciNet  Google Scholar 

  17. B. I. Plotkin, “Radical Groups,” Amer. Math. Soc. Transl. 17(2), 9–28 (1961).

    MathSciNet  Google Scholar 

  18. C. C. Chang and H. J. Keisler, Model Theory, Stud. Logic Found. Math. (North-Holland, Amsterdam, 1973), Vol. 73.

    Google Scholar 

  19. G. Higman, B. H. Neumann, and H. Neumann, “Embedding Theorems for Groups,” J. London Math. Soc. 24(4), 247–254 (1949).

    Article  MathSciNet  Google Scholar 

  20. A. G. Kurosh, Group Theory (Nauka, Moscow, 1967) [in Russian].

    MATH  Google Scholar 

  21. P. Hall, “Some Constructions for Locally Finite Groups,” J. London Math. Soc. 34(3), 305–319 (1959).

    Article  MathSciNet  MATH  Google Scholar 

  22. O. H. Kegel, “Regular Limits of Infinite Symmetric Groups,” in Ischia Group Theory 2008 (World Sci., Hackensack, N.J., 2009), pp. 120–130.

    Chapter  Google Scholar 

  23. B. H. Neumann, “An Essay on Free Products of Groups with Amalgamation,” Philos. Trans. Roy. Soc. London. Ser. A 246, 503–554 (1954).

    Article  MathSciNet  MATH  Google Scholar 

  24. L. Henkin, J. D. Monk, and A. Tarski, Cylindric Algebras, I, Stud. Logic Found. Math. (North-Holland, Amsterdam, 1985), Vol. 64; Cylindric Algebras, II, Stud. Logic Found. Math. (North-Holland, Amsterdam, 1985), Vol. 115.

    Google Scholar 

  25. B. I. Plotkin, “Algebras with the Same Algebraic Geometry,” Proc. Steklov Inst.Math. 242, 165–196 (2003); arxiv: math.GM/0210194.

    MathSciNet  Google Scholar 

  26. A. I. Mal’tsev, Algebraic Systems (Nauka, Moscow, 1970) [in Russian].

    MATH  Google Scholar 

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Authors and Affiliations

  1. Institute ofMathematics, Hebrew University of Jerusalem, Jerusalem, Israel

    B. I. Plotkin

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  1. B. I. Plotkin
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Dedicated to the 100th Anniversary of the Genius Scientist Anatolii Ivanovich Mal’tsev

Original Russian Text © B.I. Plotkin, 2011, published in Sovremennye Problemy Matematiki, 2011, Vol. 15, pp. 40–66.

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Plotkin, B.I. Isotyped Algebras. Proc. Steklov Inst. Math. 278 (Suppl 1), 91–115 (2012). https://doi.org/10.1134/S0081543812070048

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  • DOI: https://doi.org/10.1134/S0081543812070048

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