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Amalgamation, congruence-extension, and interpolation properties in algebras

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References

  1. Beth, E. W.,On Podoa’s method in the theory of definition. Nederl. Akad. Wetensch. Proc. Ser. [A],56 (1953), 330–339.

    MathSciNet  Google Scholar 

  2. Comer, S. D.,Some representation theorems and the amalgamation property in algebraic logic, Doctoral dissertation, University of Colorado, Boulder, 1967, vii +92 pp.

    Google Scholar 

  3. Comer, S. D.,Galois theory and the amalgamation property in finite dimensional cylindric algebras, Preliminary report. Notices Amer. Math. Soc.15 (1968), 103.

    Google Scholar 

  4. Comer, S. D.,Classes without the amalgamation property. Pacific J. Math.28 (1969), 309–318.

    MATH  MathSciNet  Google Scholar 

  5. Craig, W.,Linear reasoning. A new form of the Herbrand-Gentzen theorem. J. Symbolic Logic22 (1957), 250–268.

    Article  MATH  MathSciNet  Google Scholar 

  6. Craig, W.,Three uses of the Herbrand-Gentzen theorem in relating model theory and proof theory. J. Symbolic Logic22 (1957), 269–285.

    Article  MATH  MathSciNet  Google Scholar 

  7. Daigneault, A.,On automorphisms of polyadic algebras. Trans. Amer. Math. Soc.112 (1964), 84–130.

    Article  MATH  MathSciNet  Google Scholar 

  8. Daigneault, A.,Freedom in polyadic algebras and two theorems of Beth and Craig. Michigan Math. J.11 (1964), 129–135.

    Article  MATH  MathSciNet  Google Scholar 

  9. Dwinger, Ph. and Yaqub, F. M.,Generalized free products of Boolean algebras with an amalgamated subalgebra. Indag. Math.25 (1963), 225–231.

    MathSciNet  Google Scholar 

  10. Henkin, L.,An extension of the Craig-Lyndon interpolation theorem. J. Symbolic Logic28 (1963), 201–216.

    Article  MathSciNet  Google Scholar 

  11. Henkin, L., Monk, J. D. and Tarski, A.,Cylindric algebras. Part I (North-Holland Publishing Co., Amsterdam, 1971), VI+509 pp.

    Google Scholar 

  12. Grätzer, G.A new notion of independence in universal algebras. Collq. Math.17 (1967), 225–234.

    MATH  Google Scholar 

  13. Grätzer, G. and Lakser, H.,The structure of pseudo-complemented distributive lattices II. Congruence extension and amalgamation. To appear

  14. Johnson, J. S.,Amalagamation of polyadic algebras. Preliminary report. Notices Amer. Math. Soc.14 (1967), 361.

    Google Scholar 

  15. Johnson, J. S.,Amalgamation of polyadic algebras and finitizability problems in algebraic logic, Doctoral dissertation, University of Colorado, Boulder, 1968, vi + 129 pp.

    Google Scholar 

  16. Jónsson, B.,Sublattices of a free lattice. Canad. J. Math.13 (1961), 256–264.

    MATH  MathSciNet  Google Scholar 

  17. Jónsson, B.,Extensions of relational structures. The theory of models, Proceedings of the 1963 International Symposium at Berkeley, ed. J. W. Addison, L. Henkin, and A. Tarski, North-Holland Publishing Co., Amsterdam, 1965, pp. 146–157.

    Google Scholar 

  18. Keisler, H. J.,Universal homogeneous Boolean algebras. Mich. Math. J.,13 (1966), 129–132.

    Article  MATH  MathSciNet  Google Scholar 

  19. Lyndon, R. C.,Metamathematics and algebra: an example. Logic, Methodology and Philosophy of Science, Proceedings of the 1960 International Congress, ed. E. Nagel, P. Suppes, and A. Tarski, Stanford University Press, Stanford, 1962, pp. 143–150.

    Google Scholar 

  20. Lyndon, R. C.,Dependence in groups. Colloq. Math.,14 (1966), 275–283.

    MATH  MathSciNet  Google Scholar 

  21. Magnus, W.,Über diskontinuierliche Gruppen mit einer definierenden Relation. (Der Freiheitssatz). J. Reine Angew. Math.,163 (1930), 141–165.

    MATH  Google Scholar 

  22. Monk, J. D.,On the representation theory for cylindric algebras. Pacific J. Math.11 (1961), 1447–1457

    MATH  MathSciNet  Google Scholar 

  23. Preller, A.,Interpolation et amalgamation, Publications du Départment de Math⨼atiques. Faculté des Sciences of Lyon. (Lyon),6, no. 1 (1969), 49–65.

    MATH  MathSciNet  Google Scholar 

  24. Robinson, A.,A result on consistency and its application to the theory of definition. Nederl. Akad. Wetensch. Proc. Ser. [A],59 (1956), 47–58.

    Google Scholar 

  25. Sikorski, R.,Products of abstract algebras. Fund. Math.39 (1952), 211–228.

    MathSciNet  Google Scholar 

  26. Tarski, A.,A representation theorem for cylindric algebras. Preliminary report. Bull. Amer. Math. Soc.,58 (1952), 65–66.

    Google Scholar 

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To my brother Leo

This paper is a revised version of the author’s doctoral dissertation submitted to the University of California. It is the result of an immensely enjoyable journey in the land between algebra and logic. The author wishes to express his gratitude to his guide on this journey, Professor Alfred Tarski, for his wit, his wisdom, and especially his patience. He also wishes to thank Professors Leon Henkin and Donald Monk for their advice and encouragement.

The research for this paper was supported by grants from the National Science Foundation.

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Pigozzi, D. Amalgamation, congruence-extension, and interpolation properties in algebras. Algebra Univ. 1, 269–349 (1971). https://doi.org/10.1007/BF02944991

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