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.
Publié le : 1992-03-14
Classification:
Definability,
algebraic integer ring,
algebraic number field,
03C40
@article{1183743887,
author = {Tung, Shih Ping},
title = {Arithmetic Definability by Formulas with Two Quantifiers},
journal = {J. Symbolic Logic},
volume = {57},
number = {1},
year = {1992},
pages = { 1-11},
language = {en},
url = {http://dml.mathdoc.fr/item/1183743887}
}
Tung, Shih Ping. Arithmetic Definability by Formulas with Two Quantifiers. J. Symbolic Logic, Tome 57 (1992) no. 1, pp. 1-11. http://gdmltest.u-ga.fr/item/1183743887/