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Source. Theorem 1, p. 7, of Robert V. Moody, Model Sets: A Survey, in From Quasicrystals to More Complex Systems (Les Houches School lecture notes), Springer/EDP Sciences (2000), 145-166, doi:10.1007/978-3-662-04253-3_6, read in the preprint arXiv:math/0002020v1 (2 Feb 2000) named on the source card; pages here are that preprint's pages, and the book pagination was not compared.

Read depth. Claims checked: the statement and the definitions it uses were read on the printed pages. The survey gives no proof. Nothing here is independently reviewed.

Statement

Setting. A Meyer set is a Delone set $\Lambda\subset\mathbb R^d$ with $\Lambda-\Lambda$ uniformly discrete (p. 7, display (6)); model sets are as in the definitions of Section 2, with internal space any locally compact abelian group.

Theorem 1 (p. 7, quoted). "Any Meyer set is a Delone subset of some model set."

The survey attributes the theorem to Y. Meyer, Algebraic numbers and harmonic analysis, North-Holland (1972), its reference [25]. Section 7.1 (p. 24) cites the theorem as the reason the embedding space $\mathbb R^d\times G$ with $G$ locally compact abelian is natural.

Proof pointer

No proof is given in the survey; it points to Meyer's book.

Dependencies

The definitions of model sets of Section 2.

Bears on

• Problem 188: the paper does not mention the problem. It is a survey of the cut-and-project construction of aperiodic point sets; it says nothing about unit distances, two-colorings of the plane or arithmetic progressions, and gives no coloring and no bound on the number of terms the problem asks about.