David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 50 (1):59-71 (1985)
S. Ulam asked about the number of nonisomorphic projective algebras with k generators. This paper answers his question for projective algebras of finite dimension at least three and shows that there are the maximum possible number, continuum many, of nonisomorphic one-generated structures of finite dimension n, where n is at least three, of the following kinds: projective set algebras, projective algebras, diagonal-free cylindric set algebras, diagonal-free cylindric algebras, cylindric set algebras, and cylindric algebras. The results of this paper extend earlier results to the collection of cylindric set algebras and provide a uniform proof for all the results. Extensions of these results for dimension two are discussed where some modifications on the hypotheses are needed. Furthermore for α |geq 2, the number of isomorphism classes of regular locally finite cylindric set algebras of dimension α of the following two kinds are computed: ones of power κ for infinite $\kappa \geq|\alpha|$ , and ones with a single generator
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Robin Hirsch, Ian Hodkinson & Roger D. Maddux (2002). Relation Algebra Reducts of Cylindric Algebras and an Application to Proof Theory. Journal of Symbolic Logic 67 (1):197-213.
Yde Venema (1995). Cylindric Modal Logic. Journal of Symbolic Logic 60 (2):591-623.
Tarek Sayed Ahmed & Istvan Németi (2001). On Neat Reducts of Algebras of Logic. Studia Logica 68 (2):229-262.
Vera Stebletsova & Yde Venema (2001). Undecidable Theories of Lyndon Algebras. Journal of Symbolic Logic 66 (1):207-224.
I. Németi & A. Simon (2009). Weakly Higher Order Cylindric Algebras and Finite Axiomatization of the Representables. Studia Logica 91 (1):53 - 62.
B. Biró & S. Shelah (1988). Isomorphic but Not Lower Base-Isomorphic Cylindric Set Algebras. Journal of Symbolic Logic 53 (3):846-853.
Gábor Sági (2000). A Completeness Theorem for Higher Order Logics. Journal of Symbolic Logic 65 (2):857-884.
Leon Henkin (1971). Cylindric Algebras. Amsterdam,North-Holland Pub. Co..
Maarten Marx & Szabolcs Mikulás (1999). Decidability of Cylindric Set Algebras of Dimension Two and First-Order Logic with Two Variables. Journal of Symbolic Logic 64 (4):1563-1572.
Roger D. Maddux (1989). Nonfinite Axiomatizability Results for Cylindric and Relation Algebras. Journal of Symbolic Logic 54 (3):951-974.
Added to index2009-01-28
Total downloads8 ( #276,630 of 1,726,249 )
Recent downloads (6 months)1 ( #369,877 of 1,726,249 )
How can I increase my downloads?