DOP and FCP in generic structures

1996/07/15 by John T. Baldwin, Saharon Shelah, Baldwin, John T. +1
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Limits and Structures in Graph Theory #Logic (math.LO) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.math/9607228

openalex publication_date 1996/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Spencer and Shelah [ShSp:304] constructed for each irrational alpha between 0 and 1 the theory T^alpha as the almost sure theory of random graphs with edge probability n^{- alpha}. In [BlSh:528] we proved that this was the same theory as the theory T_alpha built by constructing a generic model in Baldwin and Shi. In this paper we explore some of the more subtle model theoretic properties of this theory. We show that T^alpha has the dimensional order property and does not have the finite cover property.

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