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Logic and Logical Philosophy

On the homogeneous countable Boolean contact algebra
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On the homogeneous countable Boolean contact algebra

Authors

  • Ivo Düntsch Brock University
  • Sanjiang Li University of Technology Sydney

DOI:

https://doi.org/10.12775/LLP.2013.012

Keywords

pointless geometry, Boolean contact algebra, homogeneous structure, contact relation algebra, region connection calculus

Abstract

In a recent paper, we have shown that the class of Boolean contact algebras (BCAs) has the hereditary property, the joint embedding property and the amalgamation property. By Fraïssé’s theorem, this shows that there is a unique countable homogeneous BCA. This paper investigates this algebra and the relation algebra generated by its contact relation. We first show that the algebra can be partitioned into four sets {0}, {1}, K, and L, which are the only orbits of the group of base automorphisms of the algebra, and then show that the contact relation algebra of this algebra is finite, which is the first non-trivial extensional BCA we know which has this property.

Author Biographies

Ivo Düntsch, Brock University

Dept of Computer Science

Sanjiang Li, University of Technology Sydney

Centre for Quantum Computation and Intelligent Systems

References

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Logic and Logical Philosophy

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Published

2013-06-11

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1.
DÜNTSCH, Ivo & LI, Sanjiang. On the homogeneous countable Boolean contact algebra. Logic and Logical Philosophy [online]. 11 June 2013, T. 22, nr 2, s. 213–251. [accessed 28.3.2023]. DOI 10.12775/LLP.2013.012.
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