David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Bulletin of Symbolic Logic 11 (4):465-516 (2005)
This is a survey article on algebraic logic. It gives a historical background leading up to a modern perspective. Central problems in algebraic logic (like the representation problem) are discussed in connection to other branches of logic, like modal logic, proof theory, model-theoretic forcing, finite combinatorics, and Gödel's incompleteness results. We focus on cylindric algebras. Relation algebras and polyadic algebras are mostly covered only insofar as they relate to cylindric algebras, and even there we have not told the whole story. We relate the algebraic notion of neat embeddings (a notion special to cylindric algebras) to the metalogical ones of provability, interpolation and omitting types in variants of first logic. Another novelty that occurs here is relating the algebraic notion of atom-canonicity for a class of boolean algebras with operators to the metalogical one of omitting types for the corresponding logic. A hitherto unpublished application of algebraic logic to omitting types of first order logic is given. Proofs are included when they serve to illustrate certain concepts. Several open problems are posed. We have tried as much as possible to avoid exploring territory already explored in the survey articles of Monk  and Németi  in the subject
|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
Miklós Ferenczi (2010). Non-Standard Stochastics with a First Order Algebraization. Studia Logica 95 (3):345 - 354.
Tarek Sayed Ahmed (2010). The Class of Polyadic Algebras has the Super Amalgamation Property. Mathematical Logic Quarterly 56 (1):103-112.
Tarek Sayed Ahmed (2007). A Note on Neat Reducts. Studia Logica 85 (2):139 - 151.
Tarek Sayed Ahmed (2009). A Note on Substitutions in Representable Cylindric Algebras. Mathematical Logic Quarterly 55 (3):280-287.
Mohamed Amer & Tarek Sayed Ahmed (2006). Polyadic and Cylindric Algebras of Sentences. Mathematical Logic Quarterly 52 (5):444-449.
Similar books and articles
I. Németi & A. Simon (2009). Weakly Higher Order Cylindric Algebras and Finite Axiomatization of the Representables. Studia Logica 91 (1):53 - 62.
Tarek Sayed Ahmed & Istvan Németi (2001). On Neat Reducts of Algebras of Logic. Studia Logica 68 (2):229-262.
Yde Venema (1995). Cylindric Modal Logic. Journal of Symbolic Logic 60 (2):591-623.
Gábor Sági (2000). A Completeness Theorem for Higher Order Logics. Journal of Symbolic Logic 65 (2):857-884.
B. Biró & S. Shelah (1988). Isomorphic but Not Lower Base-Isomorphic Cylindric Set Algebras. Journal of Symbolic Logic 53 (3):846-853.
István Németi (1991). Algebraization of Quantifier Logics, an Introductory Overview. Studia Logica 50 (3-4):485 - 569.
Robin Hirsch & Ian Hodkinson (1997). Step by Step-Building Representations in Algebraic Logic. Journal of Symbolic Logic 62 (1):225-279.
Roger D. Maddux (1989). Nonfinite Axiomatizability Results for Cylindric and Relation Algebras. Journal of Symbolic Logic 54 (3):951-974.
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.
Tarek Sayed Ahmed (2002). Martin's Axiom, Omitting Types, and Complete Representations in Algebraic Logic. Studia Logica 72 (2):285 - 309.
Added to index2009-01-28
Total downloads28 ( #133,846 of 1,789,824 )
Recent downloads (6 months)10 ( #82,832 of 1,789,824 )
How can I increase my downloads?