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arXiv · 2306.12011

Non-trivial higher homotopy of first-order theories

Tim Campion·Jinhe Ye
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Abstract

Let $T$ be the theory of dense cyclically ordered sets with at least two elements. We determine the classifying space of $\mathsf{Mod}(T)$ to be homotopically equivalent to $\mathbb{CP}^\infty$. In particular, $π_2(\lvert\mathsf{Mod}(T)\rvert)=\mathbb{Z}$, which answers a question in our previous work. The computation is based on Connes' cycle category $Λ$.

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Tim Campion, Jinhe Ye. 2024-01-12. Non-trivial higher homotopy of first-order theories. https://doi.org/10.1017/jsl.2024.3

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