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)
Summary
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).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have