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Structures preserved by primitive actions of $S_\omega$
arXiv:2501.03789v4 Announce Type: replace-cross Abstract: We present a dichotomy for structures $A$ that are preserved by primitive actions of $S_{\omega} = \text{Sym}({\mathbb N})$: such a structure primitively positively constructs all finite structures and the constraint satisfaction problem is NP-complete, or the constraint satisfaction problem for $A$ is in P. To prove our result, we study the first-order reducts of the Johnson graph $J(k)$, for $k \geq 2$, whose automorphism group $G$...
The Unreasonable Redundancy of Nature's Protein Folds
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