[Disclaimer: this a blog-post consciously written in the style adumbrated in Compressing and summarizing. Part 0. For the original, see https://arxiv.org/abs/1708.00148. Compression ratio here is high. ]

This reports on this recent preprint by Siddharth Baskar and Alex Kruckman.

- Loc. cit. proves that for any purely relational signature , and for any class consisting of
*finite* -structures,

has the strict order property

if and only if

uniformly interprets the natural numbers.

- I recall that a logical formula having
*the strict order property relative to a theory *means that for every model of , the poset contains arbitrarily long finite chains.

(to be continued)

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