Modeling FO-limits for monadically stable sequences
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911102914265088 |
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| author | Braunfeld, S. Nešetřil, J. de Mendez, P. Ossona |
| author_facet | Braunfeld, S. Nešetřil, J. de Mendez, P. Ossona |
| contents | 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 $σ$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_08960 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Modeling FO-limits for monadically stable sequences Braunfeld, S. Nešetřil, J. de Mendez, P. Ossona Logic Combinatorics 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 $σ$-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. |
| title | Modeling FO-limits for monadically stable sequences |
| topic | Logic Combinatorics |
| url | https://arxiv.org/abs/2508.08960 |