Decidability of the Natural Numbers with the Almost-All Quantifier
Logic
2007-05-23 v1 Mathematical Physics
math.MP
Abstract
We consider the fragment F of first order arithmetic in which quantification is restricted to ''for all but finitely many.'' We show that the integers form an F-elementary substructure of the real numbers. Consequently, the F-theory of arithmetic is decidable.
Cite
@article{arxiv.math/0602415,
title = {Decidability of the Natural Numbers with the Almost-All Quantifier},
author = {David Marker and Theodore A. Slaman},
journal= {arXiv preprint arXiv:math/0602415},
year = {2007}
}