Relation algebras from cylindric and polyadic algebras

Logic Journal of the IGPL 5 (4):575-588 (1997)

Abstract
This paper is a survey of recent results concerning connections between relation algebras , cylindric algebras and polyadic equality algebras . We describe exactly which subsets of the standard axioms for RA are needed for axiomatizing RA over the RA-reducts of CA3's, and we do the same for the class SA of semi-associative relation algebras. We also characterize the class of RA-reducts of PEA3's. We investigate the interconnections between the RA-axioms within CA3 in more detail, and show that only four implications hold between them . In the other direction, we introduce a natural CA-theoretic equation MGR+, generalization of the well-known Merrry-Go-Round equation MGR of CA-theory. We show that MGR+ is equivalent to the RA-reduct being an SA, and that MGR+ implies that the RA-reduct determines the algebra itself, while MGR is not sufficient for either of these to hold. Then we investigate how different CA's a single RRA can 'generate' in the general case. We solve the first part of Problem 11 from the 'Problem Session Paper' of [2].While proving some of the statements, for others we give only outline of proof. The paper contains several open problems. A full version of this paper is under preparation.Keywords: relation algebras, cylindric algebras, polyadic algebras, algebraic logic, arrow logic, proof theory, finite variable fragments, provability with 3 variables, non-finitizability, twisting, non-standard models, neat reducts, representability
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1093/jigpal/5.4.575
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 43,049
External links

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.

Add more references

Citations of this work BETA

A Modeltheoretic Solution to a Problem of Tarski.Tarek Sayed Ahmed - 2002 - Mathematical Logic Quarterly 48 (3):343-355.
A Note on Substitutions in Representable Cylindric Algebras.Tarek Sayed Ahmed - 2009 - Mathematical Logic Quarterly 55 (3):280-287.
Amalgamation in Relation Algebras.Maarten Marx - 1998 - Journal of Symbolic Logic 63 (2):479-484.

Add more citations

Similar books and articles

Polyadic and Cylindric Algebras of Sentences.Mohamed Amer & Tarek Sayed Ahmed - 2006 - Mathematical Logic Quarterly 52 (5):444-449.
Bare Canonicity of Representable Cylindric and Polyadic Algebras.Jannis Bulian & Ian Hodkinson - 2013 - Annals of Pure and Applied Logic 164 (9):884-906.
Relation Algebras From Cylindric Algebras, I.Robin Hirsch & Ian Hodkinson - 2001 - Annals of Pure and Applied Logic 112 (2-3):225-266.
Cylindric Algebras.Leon Henkin - 1971 - Amsterdam: North-Holland Pub. Co..

Analytics

Added to PP index
2015-02-04

Total views
4 ( #1,086,526 of 2,260,175 )

Recent downloads (6 months)
2 ( #656,535 of 2,260,175 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature