Tootfinder

On the Isomorphism Relation for Omnigenous Locally Finite Groups
Su Gao, Feng Li
https://arxiv.org/abs/2507.03907 https://arxiv.org/p…

On the Isomorphism Relation for Omnigenous Locally Finite Groups
The concept of an omnigenous locally finite group was introduced in [2] as a generalization of Hall's universal countable locally finite group. In this paper we show that the class of all countable omnigenous locally finite groups is Borel complete, hence it has the maximum Borel cardinality of isomorphism types among all countable structures. [2] M. Etedadialiabadi, S. Gao, F. Le Maître, J. Melleray, Dense locally finite subgroups of automorphism groups of ultraextensive spaces, Adv. Math. …

🇺🇦 #NowPlaying on KEXP's #SonicReducer
Slutbomb:
🎵 Commodified Identity
#Slutbomb
https://slutbomb.bandcamp.com/track/commodified-identity-3
https://open.spotify.com/track/3dGtCTPYq4YDPaX9aKHdZN

This https://arxiv.org/abs/2403.04324 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Sublinear expectation structure under countable state space
In this study, we propose the sublinear expectation structure under countable state space. To describe an interesting "nonlinear randomized" trial, based on a convex compact domain, we introduce a family of probability measures under countable state space. Corresponding the sublinear expectation operator introduced by S. Peng, we consider the related notation under countable state space. Within the countable state framework, the sublinear expectation can be explicitly calculated by a novel repe…

Lo único que vi de la despedida de Black Sabbath el fin de semana fue un pequeño extracto donde Ozzy cantaba «War Pigs» y la verdad es que se veía y escuchaba mucho mejor de lo que yo esperaba. Me alegró mucho.
Ozzy es de lo mšximo del rock. 🤘🏻
#Ozzy #OzzyOsbourne

#MadreFire
Size: 80, 480 Acres
Containment: 30%
Total Personnel: 1,472
Firefighters are strengthening containment lines throughout the northwest and north perimeters,
and mopping-up. Progress remains steady on the northeast and southwest perimeters,
with dozer operations reinforcing lines.
There is challenging terrain on the southwest side and crews are putting in…

Existentially closed measure-preserving actions of approximately treeable groups
Isaac Goldbring, Brandon Seward, Robin Tucker-Drob
https://arxiv.org/abs/2507.03195

Existentially closed measure-preserving actions of approximately treeable groups
Given a countable group $Γ$, letting $\mathcal{K}_Γ$ denote the class of {\pmp} actions of $Γ$, we study the question of when the model companion of $\mathcal{K}_Γ$ exists. Berenstein, Henson, and Ibarlucía showed that the model companion of $\mathcal{K}_Γ$ exists when $Γ$ is a nonabelian free group on a countable number of generators. We significantly generalize their result by showing that the model companion of $\cal K_Γ$ exists whenever $Γ$ is an approximately treeable group. The c…

Centific, an AI "data foundry" that works with businesses to develop, train, and deploy their AI models, raised a $60M Series A led by Granite Asia (Nicholas Gordon/Fortune)
https://fortune.com/asia/2025/06/25/centi…

Singapore VC Granite Asia leads $60 million funding round for AI ‘data foundry’ Centific to fund global expansion
“This funding round isn’t about necessity—it’s about ambition,” CEO Venkat Rangapuram said in a statement.

Dense and comeager conjugacy classes in zero-dimensional dynamics
Michal Doucha, Julien Melleray, Todor Tsankov
https://arxiv.org/abs/2507.05474 https://…

Dense and comeager conjugacy classes in zero-dimensional dynamics
Let $G$ be a countable group. We consider the Polish space of all actions of $G$ on the Cantor space by homeomorphisms and study the existence of a comeager conjugacy class in this space and some natural subspaces. We also develop a general model-theoretic framework to study this and related questions. We prove that for a finitely generated free group, there is a comeager conjugacy class in the space of minimal actions, as well as in the space of minimal, probability measure-preserving action…

Computable presentations of randomizations
Nicol\'as Cuervo Ovalle, Isaac Goldbring
https://arxiv.org/abs/2506.06187 https://arxi…

Computable presentations of randomizations
We initiate the effective metric structure theory of Keisler randomizations. We show that a classical countable structure $\mathcal{M}$ has a decidable presentation if and only if its Borel randomization $\mathcal{M}^{[0,1)}$ has a computable presentation for which the constant functions are uniformly computable points. We determine a sufficient condition for which the uniform computability of the constant functions can be dropped. We show that when $\mathcal{M}$ is effectively $ω$-categorical…

Permutation Models Arising From Topological Ideals
Justin Young
https://arxiv.org/abs/2507.05371 https://arxiv.org/pdf/2507.05371

Permutation Models Arising From Topological Ideals
A recent paper by Zapletal arXiv:2404.10612 discusses permutation models of set theory which arise from dynamical ideals and highlights properties of the dynamical ideal which relate to fragments of choice in the permutation model. In this paper, we provide several examples from topology which illustrate using these connections to argue that the corresponding permutation model satisfies either the axiom of countable choice or well-ordered choice.