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arXiv · 2508.08960

Modeling FO-limits for monadically stable sequences

S. Braunfeld·J. Nešetřil·P. Ossona de Mendez
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Abstract

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 $\sigma$-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.

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BibTeXRIS

S. Braunfeld, J. Nešetřil, P. Ossona de Mendez. 2025-08-12. Modeling FO-limits for monadically stable sequences. https://arxiv.org/abs/2508.08960

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