Canonical relativized cylindric set algebras

Maddux, Roger D.

doi:10.1090/S0002-9939-1989-0987611-5

Canonical relativized cylindric set algebras

Author: Roger D. Maddux
Journal: Proc. Amer. Math. Soc. 107 (1989), 465-478
MSC: Primary 03G15
DOI: https://doi.org/10.1090/S0002-9939-1989-0987611-5
MathSciNet review: 987611
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For every suitable relational structure there is a canonical relativized cylindric set algebra. This construction is used to obtain a generalization of Resek’s relative representation theorem, and a stronger version of the "Stone type representation theorem" by Andréka and Thompson.

H. Andréka and R. J. Thompson, Stone type representation theorem for algebras of relations of higher rank, Trans. Amer. Math. Soc. (to appear).

Leon Henkin and Diane Resek, Relativization of cylindric algebras, Fund. Math. 82 (1974/75), 363–383. MR 366659, DOI https://doi.org/10.4064/fm-82-4-363-383
Leon Henkin, J. Donald Monk, and Alfred Tarski, Cylindric algebras. Part I, Studies in Logic and the Foundations of Mathematics, vol. 64, North-Holland Publishing Co., Amsterdam, 1985. With an introductory chapter: General theory of algebras; Reprint of the 1971 original. MR 781929
Leon Henkin, J. Donald Monk, and Alfred Tarski, Cylindric algebras. Part I, Studies in Logic and the Foundations of Mathematics, vol. 64, North-Holland Publishing Co., Amsterdam, 1985. With an introductory chapter: General theory of algebras; Reprint of the 1971 original. MR 781929
Roger Maddux, Some varieties containing relation algebras, Trans. Amer. Math. Soc. 272 (1982), no. 2, 501–526. MR 662049, DOI https://doi.org/10.1090/S0002-9947-1982-0662049-7
Roger D. Maddux, Nonfinite axiomatizability results for cylindric and relation algebras, J. Symbolic Logic 54 (1989), no. 3, 951–974. MR 1011183, DOI https://doi.org/10.2307/2274756

I. Németi, Free Algebras and Decidability in Algebraic Logic, Doctoral dissertation, Hungarian Academy of Sciences, Budapest, 1986.

D. Resek, Some results on relativized cylindric algebras, Doctoral dissertation, University of California, Berkeley, 1975, iii+290.

Richard J. Thompson, Noncommutative cylindric algebras and relativizations of cylindric algebras, Polish Acad. Sci. Inst. Philos. Sociol. Bull. Sect. Logic 17 (1988), no. 2, 75–81. MR 974075