2 problems

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The conjecture on the necessity of $(2^{\aleph_0})^+$ -completeness for irreducible dividing-lines
Let $\mathbb{T}$ be ordered by $\leq_\mathrm{lc+}$ , and let $\mathC\subseteq\mathbb{T}$ be an irreducible, or complete prime filter, class. The completeness axiom for $\mathC$ requ…
Conjectureopendividing-lines model-theory order-theoryarXiv 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

The conjecture on the necessity of (2ℵ0)+(2^{\aleph_0})^+(2ℵ0​)+-completeness for irreducible dividing-lines