## Journal of Symbolic Logic

### Notions of Relative Ubiquity for Invariant Sets of Relational Structures

#### Abstract

Given a finite lexicon $L$ of relational symbols and equality, one may view the collection of all $L$-structures on the set of natural numbers $\omega$ as a space in several different ways. We consider it as: (i) the space of outcomes of certain infinite two-person games; (ii) a compact metric space; and (iii) a probability measure space. For each of these viewpoints, we can give a notion of relative ubiquity, or largeness, for invariant sets of structures on $\omega$. For example, in every sense of relative ubiquity considered here, the set of dense linear orderings on $\omega$ is ubiquitous in the set of linear orderings on $\omega$.

#### Article information

Source
J. Symbolic Logic, Volume 55, Issue 3 (1990), 948-986.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183743399

Mathematical Reviews number (MathSciNet)
MR1071308

Zentralblatt MATH identifier
0726.03025

JSTOR