2 problems

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Infinite-degree conjecture for infinitely constrained free amalgamation classes
Let $\mathcal{L}$ be a finite language, let $\mathcal{F}$ be an infinite collection of finite irreducible $\mathcal{L}$ -structures such that no member of $\mathcal{F}$ embeds into…
Conjectureopenbig-ramsey-degrees fraisse-structures free-amalgamationarXiv posted 2 days ago
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Simplicity and NSOP $_3$ for free amalgamation theories
Simplicity–operatorname{NSOP}3 conjecture. Simplicity and $\operatorname{NSOP}_3$ should coincide for free amalgamation theories.
Conjectureopendividing-lines free-amalgamation model-theoryarXiv posted 2 days ago

Infinite-degree conjecture for infinitely constrained free amalgamation classes