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Source: original paper, printed pp. 529–530.

Write $\mathbb R^n\to(A,B)$ when every red-blue coloring of the whole space has a red congruent copy of $A$ or a blue congruent copy of $B$. A congruent copy is an image under a Euclidean isometry. A translate $B+t$ is more restrictive: it preserves the given orientation. No measurability or other regularity of a coloring is assumed.

Let $\ell_j=\{0,e,\ldots,(j-1)e\}$, where $|e|=1$. It contains $j$ points and $j-1$ unit gaps. A $k$-dimensional brick with positive side lengths $d_1,\ldots,d_k$ means its $2^k$ vertices, isometric to $\prod_{i=1}^k\{0,d_i\}$.

The source calls a finite configuration Ramsey when for every finite color count it is forced in some sufficiently high dimension. This is a statement about dimension as well as color count. A planar conclusion, a higher-dimensional conclusion and a translation-only conclusion must not be interchanged.

The paper's open questions describe its historical state. In particular its comments about five blue collinear points or a blue unit square in the plane do not establish the current status of Problem 188 or Problem 214.