Algebraic and model-theoretic properties of tilings

@article{Oger2004AlgebraicAM,
  title={Algebraic and model-theoretic properties of tilings},
  author={Francis Oger},
  journal={Theor. Comput. Sci.},
  year={2004},
  volume={319},
  pages={103-126}
}
We investigate the relations between the geometric properties of tilings and the algebraic and model-theoretic properties of associated relational structures. Isomorphism and local isomorphism of tilings up to translation correspond to isomorphism and elementary equivalence of relational structures. In particular, two Penrose tilings, or two Robinson tilings, are elementarily equivalent. Classical results concerning the local isomorphism property and the “extraction preorder” for tilings are… CONTINUE READING

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