Tootfinder

The number of countable models of first-order theories
Anand Pillay, Predrag Tanovi\'c
https://arxiv.org/abs/2508.06854 https://arxiv.org/pdf/2508.0685…

The number of countable models of first-order theories
Throughout, $T$ denotes a complete first-order theory in a countable language $L$ that has infinite models and $I(\aleph_0,T)$ denotes the number of countable models of $T$, up to an isomorphism. To determine $I(\aleph_0,T)$, it suffices to consider only countable models of $T$ with domain $ω$; since there are at most continuum many $L$-structures with domain $ω$, $I(\aleph_0,T)\leqslant 2^{\aleph_0}$ holds. Theories with $I(\aleph_0,T)=1$ are the $\aleph_0$-categorical theories. These includ…

from my link log —
CandyFab: a DIY 3D sugar printer.
https://candyfab.org/
saved 2024-12-20 https://dotat.at/:/3D5SH.html

Some remarks on decay in countable groups and amalgamated free products
Srivatsav Kunnawalkam Elayavalli, Gregory Patchell, Lizzy Teryoshin
https://arxiv.org/abs/2509.08754 http…

Some remarks on decay in countable groups and amalgamated free products
In this note, we first study the notion of subexponential decay (SD) for countable groups with respect to a length function, which generalizes the well-known rapid decay (RD) property, first discovered by Haagerup in 1979. Several natural properties and examples are studied, especially including groups that have SD, but not RD. This consideration naturally has applications in $C^*$-algebras. We also consider in this setting a permanence theorem for decay in amalgamated free products (proved als…

Long-term behavior of the master equation on countable system space and approximation method of the (stationary) solutions via finite subsystems in the thermodynamic limit
Bernd Michael Fernengel, Thilo Gross, Wolfram Just
https://arxiv.org/abs/2508.05665

Long-term behavior of the master equation on countable system space and approximation method of the (stationary) solutions via finite subsystems in the thermodynamic limit
The Master equation - also called the differential Chapman-Kolmogorov equation - is a linear differential equation, which describes the probability evolution in a discrete system. While this is well understood, if the underlying state space is finite, the mathematics required for the treatment of infinite dimensional systems is way more complicated and advanced. In this paper we provide sufficient criteria for the rates, which guarantee that the infinite dimensional master equation is both we…

Strategy Method Effects in Centipede Games: An Optimal Design Approach
Shiang-Hung Hu, Po-Hsuan Lin, Thomas R. Palfrey, Joseph Tao-yi Wang, Yu-Hsiang Wang
https://arxiv.org/abs/2508.06425

Strategy Method Effects in Centipede Games: An Optimal Design Approach
We explore the twin questions of when and why the strategy method creates behavioral distortions in the elicitation of choices in laboratory studies of sequential games. While such distortions have been widely documented, the theoretical forces driving these distortions remain poorly understood. In this paper, we compare behavior in six optimally designed centipede games, implemented under three different choice elicitation methods: the direct response method, the reduced strategy method and th…

ClauseLens: Clause-Grounded, CVaR-Constrained Reinforcement Learning for Trustworthy Reinsurance Pricing
Stella C. Dong, James R. Finlay
https://arxiv.org/abs/2510.08429 https:/…

ClauseLens: Clause-Grounded, CVaR-Constrained Reinforcement Learning for Trustworthy Reinsurance Pricing
Reinsurance treaty pricing must satisfy stringent regulatory standards, yet current quoting practices remain opaque and difficult to audit. We introduce ClauseLens, a clause-grounded reinforcement learning framework that produces transparent, regulation-compliant, and risk-aware treaty quotes. ClauseLens models the quoting task as a Risk-Aware Constrained Markov Decision Process (RA-CMDP). Statutory and policy clauses are retrieved from legal and underwriting corpora, embedded into the agent'…

Isomorphism of almost locally compact Polish metric structures
Maciej Malicki
https://arxiv.org/abs/2508.07765 https://arxiv.org/pdf/2508.07765

Isomorphism of almost locally compact Polish metric structures
A topological space is almost locally compact if it contains a dense locally compact subspace. We generalize a result from \cite{Ma}, showing that isomorphism on Borel classes of almost locally compact Polish metric structures is always classifiable by countable structures. This allows to remove a gap in the proof presented in \cite{Ma} of a positive answer to a question of Gao and Kechris, who asked whether isometry of locally compact Polish metric spaces is classifiable by countable structure…

Metric criteria for fixed price of countable groups
Erin Bevilacqua, Lewis Bowen
https://arxiv.org/abs/2510.05459 https://arxiv.org/pdf/2510.05459

Metric criteria for fixed price of countable groups
We establish general criteria for a countable group $Γ$ to have fixed price 1 depending on a choice of left-invariant proper metric on $Γ$. We apply this criterion to show that if $Γ_1,Γ_2$ are two countable groups satisfying a certain growth condition then $Γ_1\times Γ_2$ has fixed price 1. For example, $Γ\times Γ$ has fixed price 1 for any countable group $Γ$.

Extensive embeddings into Fra\"{i}ss\'{e} structures and stationary weak independence relations
Aleksandra Kwiatkowska, Rob Sullivan, Jeroen Winkel
https://arxiv.org/abs/2508.06370

Extensive embeddings into Fraïssé structures and stationary weak independence relations
Let $M$ be a Fraïssé structure (a countably infinite ultrahomogeneous structure). We call an embedding $f : A \to M$ extensive if each automorphism of its image extends to an automorphism of $M$, where the extension map respects composition. We consider which Fraïssé structures $M$ have the property that each substructure admits an extensive embedding into $M$. We also consider which Fraïssé structures have a stationary weak independence relation (SWIR) as defined by Li, and discuss the r…

Borel distinguishing number
Onur Bilge, Burak Kaya
https://arxiv.org/abs/2508.08201 https://arxiv.org/pdf/2508.08201

Borel distinguishing number
In this paper, we study definable variants of the notion of the distinguishing number of a graph in descriptive set theoretic setting. We introduce the notion of the Borel distinguishing number of a Borel graph and provide examples that separate distinguishing number and Borel distinguishing number at various levels. More specifically, we prove that there exist Borel graphs with countable distinguishing number but uncountable Borel distinguishing number and that, for every integer $n \geq 3$, t…