Expansions and restrictions of structures and theories, their hierarchies

2025/02/05 by Sudoplatov, Sergey V.
#03C30 #03C45 #03C52 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2502.03051

Abstract

We introduce and study some general principles and hierarchical properties of expansions and restrictions of structures and their theories The general approach is applied to describe these properties for classes of ω-categorical theories and structures, Ehrenfeucht theories and their models, strongly minimal, ω₁-theories, and stable ones.

Related

• Formulas and properties
• Limiting theories of substructures
• Definable families of theories, related calculi and ranks
• Higher Algebraic Structures and General Field Theories
• A Higher Structure Identity Principle