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Arithmetic definability by formulas with two quantifiers

Published online by Cambridge University Press:  12 March 2014

Shih Ping Tung
Shih Ping Tung*
Affiliation:
Department of Mathematics, Chung Yuan Christian University, Chung Li, Taiwan 32023, Republic of China
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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, N is not definable by such a formula over Z. This extends a previous result of R. M. Robinson.

Keywords

Definabilityalgebraic integer ringalgebraic number field
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 57 , Issue 1 , March 1992 , pp. 1 - 11
Copyright
Copyright © Association for Symbolic Logic 1992

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References

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