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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.11432 |
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| _version_ | 1866908829292167168 |
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| author | Baldwin, John Nagloo, Joel |
| author_facet | Baldwin, John Nagloo, Joel |
| contents | Let $Γ\subset PSL_2(\mathbb{R})$ be a non-arithmetic Fuchsian group of the first kind with finite covolume, and let $j_Γ$ be a corresponding uniformizer. In this paper we introduce a natural $L_{ω_1,ω}$-axiomatization $T^{\infty}_{SF}$ of the theory of $j_Γ$ viewed as a covering map. We show that $T^{\infty}_{SF}$ is categorical in all infinite cardinalities, extending to the non-arithmetic setting earlier results of Daw and Harris obtained in the arithmetic case. We also show that the associated first-order theory $T_{j_Γ}$ is complete, admits elimination of quantifiers, and is $ω$-stable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_11432 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Categoricity and non-arithmetic Fuchsian groups Baldwin, John Nagloo, Joel Logic 03C35, 03C10, 33E30 Let $Γ\subset PSL_2(\mathbb{R})$ be a non-arithmetic Fuchsian group of the first kind with finite covolume, and let $j_Γ$ be a corresponding uniformizer. In this paper we introduce a natural $L_{ω_1,ω}$-axiomatization $T^{\infty}_{SF}$ of the theory of $j_Γ$ viewed as a covering map. We show that $T^{\infty}_{SF}$ is categorical in all infinite cardinalities, extending to the non-arithmetic setting earlier results of Daw and Harris obtained in the arithmetic case. We also show that the associated first-order theory $T_{j_Γ}$ is complete, admits elimination of quantifiers, and is $ω$-stable. |
| title | Categoricity and non-arithmetic Fuchsian groups |
| topic | Logic 03C35, 03C10, 33E30 |
| url | https://arxiv.org/abs/2602.11432 |