Abstract

Positive families and Boolean chains of copies of ultrahomogeneous structures

Highlights

  • The purpose of this short note is twofold

  • We show that a countable ultrahomogeneous relational structure X has the strong amalgamation property iff the set P(X)={A ⊂ X : A∼=X} contains a positive family

  • There are ultrahomogeneous structures without non-trivial copies. This kind of obstruction does not exist in the class of countable ultrahomogeneous relational structures whose age satisfies the strong amalgamation property (SAP)

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Summary

Introduction

The purpose of this short note is twofold. One is to present some new results about positive families. We show that a countable ultrahomogeneous relational structure X has the strong amalgamation property iff the set P(X)={A ⊂ X : A∼=X} contains a positive family. This kind of obstruction does not exist in the class of countable ultrahomogeneous relational structures whose age satisfies the strong amalgamation property (SAP).

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