The canonical FEP construction

The canonical FEP construction AbstractA class K of algebras has the finite embeddability property (FEP) if every finite partial subalgebra of some member of K can be embedded into some finite member of K. We prove the FEP for varieties of decreasing residuated lattice-ordered algebras using a construction based on the canonical extension. This construction produces a (generally) different finite member of the class from alternative FEP constructions for similar classes of algebras. Additionally, the constructed algebra is internally compact, in contrast to other FEP constructions. We give a description of the σ- and π-extensions of operations that do not rely on the notions of closed and open elements and we use this to obtain a syntactic description of a class of inequalities s≤t that are preserved by the construction. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Logic and Computation Oxford University Press

The canonical FEP construction

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Publisher
Oxford University Press
Copyright
© The Author, 2015. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com
ISSN
0955-792X
eISSN
1465-363X
D.O.I.
10.1093/logcom/exu080
Publisher site
See Article on Publisher Site

Abstract

AbstractA class K of algebras has the finite embeddability property (FEP) if every finite partial subalgebra of some member of K can be embedded into some finite member of K. We prove the FEP for varieties of decreasing residuated lattice-ordered algebras using a construction based on the canonical extension. This construction produces a (generally) different finite member of the class from alternative FEP constructions for similar classes of algebras. Additionally, the constructed algebra is internally compact, in contrast to other FEP constructions. We give a description of the σ- and π-extensions of operations that do not rely on the notions of closed and open elements and we use this to obtain a syntactic description of a class of inequalities s≤t that are preserved by the construction.

Journal

Journal of Logic and ComputationOxford University Press

Published: Apr 1, 2017

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