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Partial orders induced by quasilinear clones

Lehtonen, Erkko; Szendrei, Ágnes

Proceedings of the Salzburg Conference 2011 (AAA81), Verlag Johannes Heyn, Klagenfurt, (2012), 51-84

We find sufficient conditions for a subclone C of Burle's clone and for a subclone of the polynomial clone of a finite semimodule to have the property that the associated C-minor partial order has finite principal ideals. We also prove that for these clones the C-minor partial order is universal for the class of countable partial orders whose principal ideals are finite.