Distributions of countable models of theories with continuum many types

TL;DR

This paper investigates the distribution and structural properties of countable models in complete theories that have continuum many types, focusing on prime, limit, and other models relative to Rudin-Keisler preorders.

Contribution

It introduces a detailed analysis of the distributions of countable models and their structural characteristics in theories with continuum many types, expanding understanding of their model-theoretic complexity.

Findings

Distribution patterns of prime models over finite sets

Structural characteristics of limit models over types

Relationships between models and Rudin-Keisler preorders

Abstract

We present distributions of countable models and correspondent structural characteristics of complete theories with continuum many types: for prime models over finite sets relative to Rudin-Keisler preorders, for limit models over types and over sequences of types, and for other countable models of theory.