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BLAST 2008
August 6-10, 2008
University of Denver
Denver, CO, USA

Organizers
Rick Ball, Natasha Dobrinen (co-chair), Nikolaos Galatos (co-chair)

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On Full Networks and the Galois Connection between Clones and Co-clones
by
Matthew Cook
Uni-ETH Zurich / Caltech

The classic result from Geiger (1968) and Bodnarchuk et al. (1969) is that the lattices (ordered by set inclusion) of clones (closed sets of functions) and co-clones (closed sets of relations) are identical but flipped. We define a "full network" for a set of available relations, and show how it greatly simplifies the process of testing the implementability of a target relation, and it also greatly simplifies this classic (but lengthy) proof.

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Date received: June 10, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caxi-38.