Generalized amalgamation and homogeneity

TL;DR

This paper proves that certain 2-transitive finitely homogeneous structures with supersimple theories and generalized amalgamation are essentially random, extending previous results to non-binary structures and exploring their logical properties.

Contribution

It generalizes Koponen's result from binary to arbitrary structures and links generalized amalgamation with triviality and quantifier elimination in simple theories.

Findings

Structures with specified properties are shown to be random.

Extension of Koponen's result to non-binary structures.

Connection between amalgamation, triviality, and quantifier elimination.

Abstract

In this paper we shall prove that any $2$-transitive finitely homogeneous structure with a supersimple theory satisfying a generalized amalgamation property is a random structure. In particular, this adapts a result of Koponen for binary homogeneous structures to arbitrary ones without binary relations. Furthermore, we point out a relation between generalized amalgamation, triviality and quantifier elimination in simple theories.