arXiv:math/0602415 Abstract

arXiv:math/0602415 [math.LO]Abstract References Reviews Resources

Decidability of the Natural Numbers with the Almost-All Quantifier

Published 2006-02-20Version 1

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.

Categories: math.LO, math-ph, math.MP

Subjects: 03F30

Keywords: natural numbers, almost-all quantifier, decidability, first order arithmetic, f-elementary substructure

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