David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 60 (2):591-623 (1995)
Treating the existential quantification ∃ν i as a diamond $\diamond_i$ and the identity ν i = ν j as a constant δ ij , we study restricted versions of first order logic as if they were modal formalisms. This approach is closely related to algebraic logic, as the Kripke frames of our system have the type of the atom structures of cylindric algebras; the full cylindric set algebras are the complex algebras of the intended multidimensional frames called cubes. The main contribution of the paper is a characterization of these cube frames for the finite-dimensional case and, as a consequence of the special form of this characterization, a completeness theorem for this class. These results lead to finite, though unorthodox, derivation systems for several related formalisms, e.g. for the valid n-variable first order formulas, for type-free valid formulas and for the equational theory of representable cylindric algebras. The result for type-free valid formulas indicates a positive solution to Problem 4.16 of Henkin, Monk and Tarski 
|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
Tarek Sayed Ahmed (2011). On the Complexity of Axiomatizations of the Class of Representable Quasi‐Polyadic Equality Algebras. Mathematical Logic Quarterly 57 (4):384-394.
Similar books and articles
Robin Hirsch & Ian Hodkinson (1997). Step by Step-Building Representations in Algebraic Logic. Journal of Symbolic Logic 62 (1):225-279.
Leon Henkin (1971). Cylindric Algebras. Amsterdam,North-Holland Pub. Co..
Maarten de Rijke & Yde Venema (1995). Sahlqvist's Theorem for Boolean Algebras with Operators with an Application to Cylindric Algebras. Studia Logica 54 (1):61-78.
Tarek Sayed Ahmed (2005). Algebraic Logic, Where Does It Stand Today? Bulletin of Symbolic Logic 11 (4):465-516.
I. Németi & A. Simon (2009). Weakly Higher Order Cylindric Algebras and Finite Axiomatization of the Representables. Studia Logica 91 (1):53 - 62.
Maarten De Rijke & Yde Venema (1995). Sahlqvist's Theorem for Boolean Algebras with Operators with an Application to Cylindric Algebras. Studia Logica 54 (1):61 - 78.
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.
Jean A. Larson (1985). The Number of One-Generated Cylindric Set Algebras of Dimension Greater Than Two. Journal of Symbolic Logic 50 (1):59-71.
Tarek Sayed Ahmed (2002). Martin's Axiom, Omitting Types, and Complete Representations in Algebraic Logic. Studia Logica 72 (2):285 - 309.
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 downloads2 ( #412,118 of 1,692,523 )
Recent downloads (6 months)1 ( #181,267 of 1,692,523 )
How can I increase my downloads?