## Notre Dame Journal of Formal Logic

### A Silver-like Perfect Set Theorem with an Application to Borel Model Theory

Joël Combase

#### Abstract

A number of results have been obtained concerning Borel structures starting with Silver and Friedman followed by Harrington, Shelah, Marker, and Louveau. Friedman also initiated the model theory of Borel (in fact totally Borel) structures. By this we mean the study of the class of Borel models of a given first-order theory. The subject was further investigated by Steinhorn. The present work is meant to go further in this direction. It is based on the assumption that the study of the class of, say, countable models of a theory reduces to analyzing a single $\omega_1$-saturated model. The question then arises as to when such a model can be totally Borel. We present here a partial answer to this problem when the theory under investigation is superstable.

#### Article information

Source
Notre Dame J. Formal Logic, Volume 52, Number 4 (2011), 415-429.

Dates
First available in Project Euclid: 4 November 2011

https://projecteuclid.org/euclid.ndjfl/1320427646

Digital Object Identifier
doi:10.1215/00294527-1499372

Mathematical Reviews number (MathSciNet)
MR2855880

Zentralblatt MATH identifier
1247.03052

#### Citation

Combase, Joël. A Silver-like Perfect Set Theorem with an Application to Borel Model Theory. Notre Dame J. Formal Logic 52 (2011), no. 4, 415--429. doi:10.1215/00294527-1499372. https://projecteuclid.org/euclid.ndjfl/1320427646