## Journal of Symbolic Logic

### Relational Structures Determined by Their Finite Induced Substructures

#### Abstract

A countably infinite relational structure $M$ is called absolutely ubiquitous if the following holds: whenever $N$ is a countably infinite structure, and $M$ and $N$ have the same isomorphism types of finite induced substructures, there is an isomorphism from $M$ to $N$. Here a characterisation is given of absolutely ubiquitous structures over languages with finitely many relation symbols. A corresponding result is proved for uncountable structures.

#### Article information

Source
J. Symbolic Logic, Volume 53, Issue 1 (1988), 222-230.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183742577

Mathematical Reviews number (MathSciNet)
MR929387

Zentralblatt MATH identifier
0647.03022

JSTOR