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Journal of the London Mathematical Society 1996 54(2):210-226; doi:10.1112/jlms/54.2.210
© 1996 by London Mathematical Society
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© The London Mathematical Society

Splitting of Finite Covers of N0-Categorical Structures

David M. Evans

School of Mathematics, University of East Anglia Norwich NR4 7TJ E-mail: D.Evans{at}uea.ac.uk

Received 14 September 1993. Revision received 27 February 1995.

Suppose that W is a countable N0-categorical structure. We investigate the question as to whether every finite cover of W splits, that is, has an expansion which is a trivial finite cover of W. We show that for most primitive structures W which are homogeneous for a single binary relation (homogeneous graphs, partial orderings, the Henson digraphs, ...) any finite cover splits. However, in contrast to this, we show that there are non-split covers (with finite kernels) of the countable, universal, homogeneous local order.


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