Modeling FO-limits for monadically stable sequences
Modeling FO-limits for monadically stable sequences
We show that given a monadically stable theory $T$, a sufficiently saturated $\mathbf M \models T$, and a coherent system of probability measures on the $Ï$-algebras generated by parameter-definable sets of $\mathbf M$ in each dimension, we may produce a totally Borel $\mathbf B \prec \mathbf M$ realizing these measures. Our main application is to prove that every FO-convergent sequence of structures (with countable signature) from a monadically stable class admits a modeling limit. As another consequence, we prove a Borel removal lemma for monadically stable Lebesgue relational structures.
S. Braunfeld、J. Nešetřil、P. Ossona de Mendez
数学
S. Braunfeld,J. Nešetřil,P. Ossona de Mendez.Modeling FO-limits for monadically stable sequences[EB/OL].(2025-08-12)[2025-08-24].https://arxiv.org/abs/2508.08960.点此复制
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