Imperial College London
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Emeritus ProfessorIanHodkinson

Faculty of Engineering, Department of Computing

Emeritus Professor of Logic and Computation
 
 
 
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Contact

 

i.hodkinson Website

 
 
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Location

 

noneHuxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Goldblatt:2017,
author = {Goldblatt, R and Hodkinson, I},
journal = {Categories and General Algebraic Structures with Applications},
pages = {9--31},
title = {Tangled closure algebras},
url = {http://hdl.handle.net/10044/1/43152},
volume = {7},
year = {2017}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - The tangled closure of a collection of subsets of a topological space is the largest subset in which each member of the collection is dense. This operation models a logical 'tangle modality' connective, of significance in finite model theory. Here we study an abstract equational algebraic formulation of the operation which generalises the McKinsey-Tarski theory of closure algebras. We show that any dissectable tangled closure algebra, such as the algebra of subsets of any metric space without isolated points, contains copies of every finite tangled closure algebra. We then exhibit an example of a tangled closure algebra that cannot be embedded into any complete tangled closure algebra, so it has no MacNeille completion and no spatial representation.
AU  - Goldblatt,R
AU  - Hodkinson,I
EP  - 31
PY  - 2017///
SN  - 2345-5853
SP  - 9
TI  - Tangled closure algebras
T2  - Categories and General Algebraic Structures with Applications
UR  - http://hdl.handle.net/10044/1/43152
VL  - 7
ER  -
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