Asymptotic Classes of Trees and ℵ₀-categoricity

2023/07/15 by Mostafa Mirabi, Mirabi, Mostafa
Computer Science · Economics, Econometrics and Finance · Physics and Astronomy · #03C13 #03C15 #03C45 #Complex Systems and Time Series Analysis #FOS: Mathematics #Logic (math.LO) #Statistical Mechanics and Entropy #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2307.07899

openalex publication_date 2023/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper focuses on the characterization of ℵ₀-categorical theories of trees in the following sense: for any ℵ₀-cateorical theory T of trees there is a tree plan Γ such that T=Th(Γ(ω)) where Γ(ω) is the generic model of a Fraïssé class K(Γ) obtained from the tree plan Γ. Also, it is shown that K(Γ) forms an asymptotic class, and its model-theoretic properties have been studied. Moreover, it is demonstrated that asymptotic classes of finite trees yield ℵ₀-categorical ultraproducts, and a characterization of supersimple, finite rank trees, using the notion of tree plan, is provided.

Related

• The ℵ₀-categorical Trees and Cycle-free Partial Orders
• Full asymptotic expansion for Polya structures
• Asymptotic Theories of Classes Defined by Forbidden Homomorphisms
• Infinite trees
• Ordered asymptotic classes of finite structures