On the number of elementary submodels of an unsuperstable homogeneous structure

1997/02/15 by Tapani Hyttinen, Saharon Shelah, Hyttinen, Tapani +1
Computer Science · Engineering · Mathematics · #Computational Geometry and Mesh Generation #FOS: Mathematics #Logic (math.LO) #Topology Optimization in Engineering #math.LO

paper · pdf · doi:10.48550/arxiv.math/9702228

published as MLQ Math. Log. Q. 44 No. 3 (1998) 354--358

arxiv created 1997/02/15 · openalex publication_date 1997/02/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that if M is a stable unsuperstable homogeneous structure, then for most kappa < |M|, the number of elementary submodels of M of power kappa is 2^kappa .

Related

• Main gap for locally saturated elementary submodels of a homogeneous\n structure
• Strong splitting in stable homogeneous models
• Uncountable homogeneous structures
• A dichotomy for the number of ultrapowers
• Binary simple homogeneous structures are supersimple with finite rank