[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)