View More View Less
  • 1 Cairo University Department of Mathematics, Faculty of Science Giza Egypt
Restricted access

Purchase article

USD  $25.00

1 year subscription (Individual Only)

USD  $800.00

Let (Kα: αω) be a system of varieties definable by schemas. We characterize the amalgamation base, strong amalgamation base, and super amalgamation base of the class \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $S\mathfrak{N}\mathfrak{r}_\alpha $ \end{document}Kα+ω at this abstract level.

  • Andréka, H., Complexity of equations valid in algebras of relations. I, Annals of Pure and Applied Logic, 89, (1997), no. 2–3, p. 149–209. MR 1490104 (99b:03078) II. MR 1490105 (99b:03079)

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

    • Search Google Scholar
  • Andréka, H., Gregely, T. and Németi, I., On universal algebraic constructions of logics, Studia Logica, 36 (1977), no. 1–2, 9–47. MR 0505485 (58#21599

    Németi I. , 'On universal algebraic constructions of logics ' (1977 ) 36 Studia Logica : 9 -47.

    • Search Google Scholar
  • Andréka, H., Monk., J.D. and Németi, I. (editors). Algebraic Logic, North-Holland, Amsterdam, 1991.

    '', in Algebraic Logic , (1991 ) -.

  • Andréka, H. and Németi, I., A simple purely algebraic proof of the completeness of some first order logics, Algebra Universalis, 5 (1975), 8–15. MR 038186 (52#2875)

    Németi I. , 'A simple purely algebraic proof of the completeness of some first order logics ' (1975 ) 5 Algebra Universalis : 8 -15.

    • Search Google Scholar
  • Andréka, H. and Németi, I., Neat reducts of varieties, Studia. Sci. Math. Hungarica., 13 (1978), no. 1, 47–51. MR 0630379 (82j:08013)

    Németi I. , 'Neat reducts of varieties ' (1978 ) 13 Studia. Sci. Math. Hungarica. : 47 -51.

  • Andréka, H. and Németi, I., On Systems of varieties definable by schemes of equations, Algebra Universalis, 11 (1980), no. 1, 105–116. MR 0593017 (82d:08007)

    Németi I. , 'On Systems of varieties definable by schemes of equations ' (1980 ) 11 Algebra Universalis : 105 -116.

    • Search Google Scholar
  • Andréka, H., Németi, I. and Sain, I., Algebraic Logic (2000). In Handbook of Philosophical Logic, Editors Gabbay et all. Vol. 2. MR 1884630

  • Blok, W. J. and Pigozzi, D., Algebraizable logics. Memoirs of American Mathematical Society, 77(396), 1989. MR 0973361 (90d:03140)

  • Comer S. D., Classes without the amalgamation property, Pacific Journal of Mathematics, 28(2) (1969), 309–318. MR 0242650 (39#3980)

    Comer S. D. , 'Classes without the amalgamation property ' (1969 ) 28 Pacific Journal of Mathematics : 309 -318.

    • Search Google Scholar
  • Henkin, L., Monk, J. D. and Tarski, A., Cylindric Algebras, Part I, North Holland, 1971. MR 0781929 (86m:03095a)

  • Henkin, L., Monk, J. D. and Tarski, A., Cylindric Algebras, Part II, North Holland, 1985. MR 0781930 (86m:03095b)

  • Madarász, J. and Sayed Ahmed, T., Neat reducts and amalgamation in retrospect, a survey of results and some methods. Part 1: Results on neat reducts, Logic Journal of IGPL, 17(4) (2009), p. 429–483. MR 2525829 (2011e:03085

    Sayed Ahmed T. , 'Neat reducts and amalgamation in retrospect, a survey of results and some methods. Part 1: Results on neat reducts ' (2009 ) 17 Logic Journal of IGPL : 429 -483.

    • Search Google Scholar
  • Marx, M., Amalgamation in finite dimensional cylindric algebras, Algebra Universalis, 43 (2000), no. 1, p. 41–49. 2000. MR 1765152 (2001h:03123)

    Marx M. , 'Amalgamation in finite dimensional cylindric algebras ' (2000 ) 43 Algebra Universalis : 41 -49.

    • Search Google Scholar
  • 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(3) (1983), pp. 399–409. MR 0703505 (85e:03156)

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

    • Search Google Scholar
  • Pigozzi, D., Amalgamation, congruence extension, and interpolation properties in algebras, Algebra Universalis, 1 (1971/72), p. 269–349. MR 0300897 (46#57)

    Pigozzi D. , 'Amalgamation, congruence extension, and interpolation properties in algebras ' (1971 ) 1 Algebra Universalis : 269 -349.

    • Search Google Scholar
  • Sain, I., On the searc for a finitizable algebraization of first order logic, Logic Journal of IGPL. Oxford University Press, 8(4) (2000), p. 495–589. MR 1776151 (2001m:03134)

    Sain I. , '' (2000 ) 8 On the searc for a finitizable algebraization of first order logic : 495 -589.

  • Sayed Ahmed, T., On Amalgamation of Reducts of Polyadic Algebras, Algebra Universalis, 51 (2004), no. 4, p. 301–359. MR 2082131 (2005e:03146)

    Sayed Ahmed T. , 'On Amalgamation of Reducts of Polyadic Algebras ' (2004 ) 51 Algebra Universalis : 301 -359.

    • Search Google Scholar
  • Sayed Ahmed, T., Tarskian Algebraic Logic, Journal on Relational Methods in Computer Science, 1 (2004), p. 3–26.

    Sayed Ahmed T. , 'Tarskian Algebraic Logic ' (2004 ) 1 Journal on Relational Methods in Computer Science : 3 -26.

    • Search Google Scholar
  • Sayed Ahmed, T., Algebraic Logic, where does it stand today? Bulletin of Symbolic Logic, 11(4) (2005), p. 465–516. MR 2198710 (2006k:03143)

    Sayed Ahmed T. , 'Algebraic Logic, where does it stand today? ' (2005 ) 11 Bulletin of Symbolic Logic : 465 -516.

    • Search Google Scholar
  • Sayed Ahmed, T., Amalgamation Theorems in Algebraic Logic, an overview, Logic Journal of IGPL, 13 (2005), no. 3, p. 277–286. MR 2157420 (2006g:03121)

    Sayed Ahmed T. , 'Amalgamation Theorems in Algebraic Logic, an overview ' (2005 ) 13 Logic Journal of IGPL : 277 -286.

    • Search Google Scholar
  • Sayed Ahmed, T., On neat embeddings of cylindric algebras, Mathematical Logic Quarterly, 55(6) (2009), 666–668. MR 2582167 (2011c:03146)

    Sayed Ahmed T. , 'On neat embeddings of cylindric algebras ' (2009 ) 55 Mathematical Logic Quarterly : 666 -668.

    • Search Google Scholar
  • Sayed Ahmed, T., The class of polyadic algebras has the superamalgamation property, Mathematical Logic Quarterly, 56(1) (2010), 103–112. MR 2598842

    Sayed Ahmed T. , 'The class of polyadic algebras has the superamalgamation property ' (2010 ) 56 Mathematical Logic Quarterly : 103 -112.

    • Search Google Scholar
  • Sayed Ahmed, T., Varietes of algebras without the amalgamation property, Logic Journal of IGPL, in press.

  • Sayed Ahmed, T., Some results on neat reducts, Algebra Universalis, in press.

  • Sayed Ahmed, T. and Németi, I, On neat reducts of algebras of logic, Studia Logica, 62(2) (2001), p. 229–262. MR 1860732 (2002h:03142)

    Németi I. , 'On neat reducts of algebras of logic ' (2011 ) 62 Studia Logica : 229 -262.

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