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Partially ordered sets and the independence property

Published online by Cambridge University Press:  12 March 2014

James H. Schmerl
James H. Schmerl*
Affiliation:
Department of Mathematics, University of Connecticut, Storrs, Connecticut 06268
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Abstract

No theory of a partially ordered set of finite width has the independence property, generalizing Poizat's corresponding result for linearly ordered sets. In fact, a question of Poizat concerning linearly ordered sets is answered by showing, moreover, that no theory of a partially ordered set of finite width has the multi-order property. It then follows that a distributive lattice is not finite-dimensional iff its theory has the independence property iff its theory has the multi-order property.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 54 , Issue 2 , June 1989 , pp. 396 - 401
Copyright
Copyright © Association for Symbolic Logic 1989

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References

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