## Journal of Symbolic Logic

### Arithmetic Definability by Formulas with Two Quantifiers

Shih Ping Tung

#### Abstract

We give necessary conditions for a set to be definable by a formula with a universal quantifier and an existential quantifier over algebraic integer rings or algebraic number fields. From these necessary conditions we obtain some undefinability results. For example, $\mathbf{N}$ is not definable by such a formula over $\mathbf{Z}$. This extends a previous result of R. M. Robinson.

#### Article information

Source
J. Symbolic Logic, Volume 57, Issue 1 (1992), 1-11.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183743887

Mathematical Reviews number (MathSciNet)
MR1150921

Zentralblatt MATH identifier
0763.03019

JSTOR