## Journal of Symbolic Logic

### Automorphism-Invariant Measures on $\aleph_0$-Categorical Structures without the Independence Property

Douglas E. Ensley

#### Abstract

We address the classification of the possible finitely-additive probability measures on the Boolean algebra of definable subsets of $M$ which are invariant under the natural action of $\operatorname{Aut}(M)$. This pursuit requires a generalization of Shelah's forking formulas [8] to "essentially measure zero" sets and an application of Myer's "rank diagram" [5] of the Boolean algebra under consideration. The classification is completed for a large class of $\aleph_0$-categorical structures without the independence property including those which are stable.

#### Article information

Source
J. Symbolic Logic, Volume 61, Issue 2 (1996), 640-652.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183745019

Mathematical Reviews number (MathSciNet)
MR1394619

Zentralblatt MATH identifier
0862.03021

JSTOR
Ensley, Douglas E. Automorphism-Invariant Measures on $\aleph_0$-Categorical Structures without the Independence Property. J. Symbolic Logic 61 (1996), no. 2, 640--652. https://projecteuclid.org/euclid.jsl/1183745019