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Decidability of the Natural Numbers with the Almost-All Quantifier

David Marker·Theodore A. Slaman
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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.

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David Marker, Theodore A. Slaman. 2006-02-20. Decidability of the Natural Numbers with the Almost-All Quantifier. https://arxiv.org/abs/math/0602415

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