Corpus ID: 189762482

Smooth digraphs modulo primitive positive constructability

@article{Bodirsky2019SmoothDM,
  title={Smooth digraphs modulo primitive positive constructability},
  author={M. Bodirsky and Florian Starke and A. Vucaj},
  journal={arXiv: Rings and Algebras},
  year={2019}
}
We consider the poset that arises from ordering finite smooth digraphs via pp-constructability. We give a complete description of this poset and, in particular, we prove that it is a distributive lattice. Moreover, we show that in order to separate two smooth digraphs in our poset it suffices to show that the polymorphism clone of one satisfies a prime cyclic loop condition that is not satisfied by the polymorphism clone of the other. 

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