ArticleOriginal scientific text

Title

What the finitization problem is not

Authors 1

Affiliations

  1. Mathematical Institute of the Hungarian Academy of Sciences, P.O. Box 127, Budapest, H-1364, Hungary

Bibliography

  1. [A91] H. Andréka, Complexity of the equations valid in algebras of relations, thesis for D.Sc. (a post-habilitation degree), Hungar. Acad. Sci., Budapest 1991.
  2. [AMN] H. Andréka, J. D. Monk and I. Németi (eds.), Algebraic Logic (Proc. Conf. Budapest 1988), Colloq. Math. Soc. János Bolyai 54, North-Holland, Amsterdam 1991.
  3. [ANS] H. Andréka, I. Németi and I. Sain, Abstract model-theoretic approach to algebraic logic, manuscript, 1984.
  4. [BF] J. Barwise and S. Feferman (eds.), Model-Theoretic Logics, Springer, Berlin 1985.
  5. [BMP] C. H. Bergman, R. D. Maddux and D. L. Pigozzi (eds.), Algebraic Logic and Universal Algebra in Computer Science, Lecture Notes in Comput. Sci. 425, Springer, Berlin 1990.
  6. [BP] W. J. Blok and D. Pigozzi, Algebraizable logics, Mem. Amer. Math. Soc. 396 (1989).
  7. [B86] P. Burmeister, A model-theoretic oriented approach to partial algebras, Akademie-Verlag, Berlin 1986.
  8. [BS] S. Burris and H. P. Sankappanavar, A Course in Universal Algebra, Springer, New York 1981.
  9. [CV] W. Craig and R. L. Vaught, Finite axiomatizability using additional predicates, J. Symbolic Logic 23 (3) (1958), 289-308.
  10. [D] M. Davis, Unsolvable Problems, in: Handbook of Mathematical Logic, J. Barwise (ed.), North-Holland, Amsterdam 1977, 567-594.
  11. [H] L. Henkin, The representation theorem for cylindric algebras, in: Mathematical Interpretations of Formal Systems, North-Holland, Amsterdam 1955, 85-97.
  12. [HM] L. Henkin and J. D. Monk, Cylindric algebras and related structures, in: Proceedings of the Tarski Symposium, Amer. Math. Soc., 1974, 105-121.
  13. [HMT] L. Henkin, J. D. Monk and A. Tarski, Cylindric Algebras, Parts I, II, North-Holland, Amsterdam 1971, 1985.
  14. [M] R. Maddux, Finitary algebraic logic, Z. Math. Logik Grundlag. Math. 35 (1989), 321-332.
  15. [M70] J. D. Monk, On an algebra of sets of finite sequences, J. Symbolic Logic 35 (1970), 19-28.
  16. [MLn] J. D. Monk, Lectures on cylindric set algebras, this volume.
  17. [N89] I. Németi, On cylindric algebraic model theory, in [BMP], 37-75.
  18. [N91] I. Németi, Algebraization of quantifier logics: an introductory overview, Studia Logica 4 (1991), in press.
  19. [S87] I. Sain, Searching for a finitizable algebraization of first order logic, submitted, 1987.
  20. [S87a] I. Sain, Positive results related to the Jónsson, Tarski-Givant representation problem, preprint, Math. Inst. Hungar. Acad. Sci., Oct. 1987.
  21. [ST] I. Sain and R. J. Thompson, Strictly finite schema axiomatization of quasi-polyadic algebras, in [AMN], 539-571.
  22. [S90] A. Simon, A complete calculus for type-free logic and representable cylindric algebras, preprint, Math. Inst. Hungar. Acad. Sci.
  23. [S91] A. Simon, Finite schema completeness for typeless logic and representable cylindric algebras, in [AMN], 665-670.
  24. [TG] A. Tarski and S. Givant, A Formalization of Set Theory without Variables, Colloq. Publ. 41, Amer. Math. Soc., 1986.
  25. [VH] P. A. S. Veloso and A. M. Haeberer, A finitary relational algebra for classical first order logic, preprint, Rio de Janeiro; abstracted in: Bull. Section of Logic 20 (2) (1991), 52-62.
  26. [ [V90] Y. Venema, Cylindric modal logic, submitted to J. Symbolic Logic.
  27. [V92] Y. Venema, Many-dimensional modal logic, Ph.D. thesis, Univ. of Amsterdam, 1992.
Pages:
95-116
Main language of publication
English
Published
1993
Exact and natural sciences