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Some results about neat reducts

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Abstract

This is a survey article on the concept of neat reducts. An old venerable idea in algebraic logic, in this paper we show why it is regaining momentum.

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References

  1. Sayed Ahmed T.: The class of neat reducts is not elementary. Logic Journal of IGPL 9, 593–628 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  2. Sayed Ahmed T.: The class of 2-dimensional neat reducts of polyadic algebras is not elementary. Fund. Math. 172, 61–81 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  3. Sayed Ahmed T.: A Model-theoretic Solution to a problem of Tarski. Mathematical Logic Quaterly 48, 343–355 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  4. Sayed Ahmed T.: Martin’s axiom, omitting types and complete representations in algebraic logic. Studia Logica 72, 1–25 (2002)

    MathSciNet  Google Scholar 

  5. Sayed Ahmed T.: Neat embeddings, interpolation, and omitting types, an overview. Notre Dame Journal of formal logic 44, 157–173 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  6. Sayed Ahmed T.: On amalgamation of reducts of polyadic algebras. Algebra Universalis 51, 301–359 (2004)

    MATH  MathSciNet  Google Scholar 

  7. Sayed Ahmed T.: Algebraic Logic, where does it stand today?. Bulletin of Symbolic Logic 11(4), 465–516 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  8. Sayed Ahmed T.: The class of infinite dimensional neat reducts of quasi-polyadic algebras is not axiomatizable. Mathematical Logic Quarterly 52, 106–112 (2006)

    Article  MATH  Google Scholar 

  9. Sayed Ahmed T.: An interpolation theorem for first order logic with infinitary predicates. Logic Journal of IGPL 15, 21–32 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  10. Sayed Ahmed T.: A note on neat reducts. Studia Logica 85, 139–151 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  11. Sayed Ahmed T.: Neat embedding is not sufficient for complete representations. Bulletin Section of Logic 36, 29–36 (2007)

    Google Scholar 

  12. Sayed Ahmed T.: The superamalgamation property via neat embeddings, and a problem of Henkin and Monk. International Journal of Algebra 2, 533–554 (2008)

    MATH  MathSciNet  Google Scholar 

  13. Sayed Ahmed T.: On complete representability of reducts of Polyadic algebras. Studia Logica 89, 325–332 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  14. Sayed Ahmed, T.: A categorical approach to amalgamation theorems. To appear in Reports on Mathematical Logic.

  15. Sayed Ahmed, T.: Confirming a Conjecture of Tarski in Algebraic Logic. To appear in Reports on Marthematical Logic.

  16. Sayed Ahmed, T.: Omitting types algebraically. To appear in International Journal of Algebra

  17. Sayed Ahmed, T.: On relation algebras with quasi-projections. Preprint

  18. Sayed Ahmed, T.: Algebras having the unique neat embedding property. Submitted.

  19. Sayed Ahmed T., Andréka H., Németi I.: Omitting types for finite variable fragments and complete representations for algebras. Journal of Symbolic Logic 73, 65–89 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  20. Sayed Ahmed T., Samir B.: A Neat embedding theorem for expansions of cylindric algebras. Logic Journal of IGPL 15, 41–51 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  21. Sayed Ahmed T., Samir B.: Omitting types for first order logic with infinitary predicates. Mathematical Logic Quarterly 53(6), 564–576 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  22. Andréka H: Complexity of equations valid in algebras of relations. Annals of Pure and Applied Logic 89, 149–209 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  23. Andréka, H., Comer, C., Madarász, J., Németi, I., Sayed Ahmed, T.: Epimorphisms in cylindric algebras. Algebra Universalis (in press).

  24. Andréka, H, Monk., J.D., Németi, I. (editors): Algebraic Logic. North-Holland, Amsterdam, (1991)

  25. Andréka H., Thompson R.J.: A stone-type representation theorem for algebras of relation of higher rank. Trans. Amer. Math. Soc. 309, 671–682 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  26. Amer M., Sayed Ahmed T.: Polyadic and cylindric algebras of sentences. Mathematical Logic Quarterly 52, 44–49 (2006)

    Google Scholar 

  27. Comer S.D.: Classes without the amalgamation property. Pacific journal of Mathematics 28(2), 309–318 (1969)

    MATH  MathSciNet  Google Scholar 

  28. Daigneault A., Monk J.D.: Representation Theory for Polyadic algebras. Fund. Math. 52, 151–176 (1963)

    MATH  MathSciNet  Google Scholar 

  29. Ellentuck E.: Categoricity regained. Journal of Symbolic Logic 41, 639–643 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  30. Fremlin D, H.: Consequences of MA. Cambridge University press. (1984)

  31. Hirsch R.: Relation algebra reducts of cylindric algebras and complete representations. Journal of Symbolic Logic 72(2), 673–703 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  32. Hircsh R., Hodkinson I.: Complete representations in algebraic logic. Journal of Symbolic Logic 62, 816–847 (1997)

    Article  MathSciNet  Google Scholar 

  33. Hirsch R., Hodkinson I., Maddux R.: Relation algebra reducts of cylindric algebras and an application to proof theory. Journal of Symbolic Logic 67, 197–213 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  34. Henkin, L., Monk, J.D., Tarski, A.: Cylindric Algebras Part I. North Holland, (1971)

  35. Henkin, L., Monk, J.D., Tarski, A.: Cylindric Algebras Part II. North Holland, (1985)

  36. Hodges, W.: Model Theory, vol 42 of Encyclopedia of mathematics and its applications. Cambridge University Press (1993)

  37. Goldblatt R., Hodkinson I., Venema Y.: Erdos graphs resolve Fine’s canonicity problem. Bulletin of Symbolic Logic 10, 186–208 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  38. Madárasz J., Sayed Ahmed T.: Amalgamation, interpolation and epimorphisms. Algebra Universalis 56(2), 179–210 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  39. Madarász J.: Interpolation and Amalgamation, pushing the Limits. Part I. Studia Logica 61, 316–345 (1998)

    Google Scholar 

  40. Maksimova L.: Amalgamation and interpolation in normal modal logics. Studia Logica 50, 457–471 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  41. Martin D.A., Solovay R.M.: Internal Cohen extensions. Ann. Mathematical Logic 2, 143–178 (1970)

    Article  MATH  MathSciNet  Google Scholar 

  42. Miller, A.: Covering 2ω with ω1 disjoint closed sets. The Kleene Symposuim (proceedings, Madison, Wisconsin, 1978). Studies in Logic and the Foundation of Mathematics, 101, North-Holland, Amsterdam, (1980), p.415–421.

  43. Miller A.: Characterization of the least cardinal for which the Baire Category Theorem fails. Proc. Amer. Math. Soc. 86, 498–502 (1982)

    MATH  MathSciNet  Google Scholar 

  44. Németi I.: The Class of Neat Reducts of Cylindric Algebras is Not a Variety But is closed w.r.t. HP. Notre Dame Journal of Formal logic 24, 399–409 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  45. Németi, I.: Algebraisation of quantifier logics, an introductory overview. Math.Inst. Budapest, Preprint, No 13-1996. A shortened version appeared in Studia Logica 50, 465-569 (1991)

  46. Pigozzi D.: Amalgamation, congruence extension, and interpolation properties in algebras. Algebra Universalis. 1, 289–349 (1971)

    Article  MathSciNet  Google Scholar 

  47. Sagi G., Shelah S.: Weak and strong interpolation for algebraic logics. Journal of Symbolic Logic. 71, 104–118 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  48. Sagi, G.: On the Finitization problem in Algebraic logic. Ph.D Dissertation. Budapest (1999)

  49. Sain, I.: Searching for a finitizable algebraization of first order logic. Logic Journal of IGPL. Oxford University Press, 4, 495–589 (2000)

  50. Sagi G, Ferenszi M.: On some developments in the representation theory of cylindric-like algebras. Algebra Universalis 55, 345–353 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  51. Simon A.: What the finitization problem is not. Algebraic methods in Logic and Computer Science, Banach Centre Publications 28, 95–116 (1996)

    Google Scholar 

  52. Simon, A.: Non-representable algebras of relations. Ph.D Dissertation. Budapest (1997).

  53. Simon A.: Connections between quasi-projective relation algebras and cylindric algebras. Algebra universalis 56, 263–302 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  54. Tarski, A., Givant, S.: A formalization of set theory without variables. Amer. Math. Soc. Colloquium Publications. 41(1987)

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Correspondence to Tarek Sayed Ahmed.

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Presented by I. Hodkinson.

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Ahmed, T.S. Some results about neat reducts. Algebra Univers. 63, 17–36 (2010). https://doi.org/10.1007/s00012-010-0062-7

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