Completion and finite embeddability property for residuated ordered algebras. |
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Authors: | C J van Alten |
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Institution: | 1. School of Computer Science, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits, 2050, South Africa
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Abstract: | A residuated ordered algebra is a partially ordered set with additional ‘residuated’ operations. A construction is presented
that, from any partial subalgebra of a residuated ordered algebra, constructs a complete algebra into which the partial subalgebra
embeds. Conditions are given under which the constructed algebra is finite whenever a finite partial subalgebra is chosen.
This implies the ‘finite embeddability property’ for the given class of residuated ordered algebras. In the case that the
whole algebra is chosen as the partial subalgebra, the construction is a completion of the underlying order of the algebra.
A scheme of inequalities is described that are shown to have the property of being preserved by the above construction. These
preservation results thus extend the results on the finite embeddability property and completion. |
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Keywords: | |
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