## Journal of Symbolic Logic

### Some Dichotomy Theorems for Isomorphism Relations of Countable Models

Su Gao

#### Abstract

Strengthening known instances of Vaught Conjecture, we prove the Glimm-Effros dichotomy theorems for countable linear orderings and for simple trees. Corollaries of the theorems answer some open questions of Friedman and Stanley in an $L_{\omega 1\omega}$-interpretability theory. We also give a survey of this theory.

#### Article information

Source
J. Symbolic Logic, Volume 66, Issue 2 (2001), 902-922.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183746481

Mathematical Reviews number (MathSciNet)
MR1833486

Zentralblatt MATH identifier
0992.03057

JSTOR